Capstone
Time Series Analysis of Corpus Christi Liquor Distribution
Jenna Ford, Christian Nava and Jonathan Tan
May 21, 2020
Read in Datasets and Combine
df_17_19 = read.csv("C:/Users/b007224/Documents/masters_in_data_science/capstone/data/Bivin CC 2017-19_updated_headings.csv")
df_15_16 = read.csv("C:/Users/b007224/Documents/masters_in_data_science/capstone/data/Bivin CC 2015-16_updated_headings.csv")
df_13_14 = read.csv("C:/Users/b007224/Documents/masters_in_data_science/capstone/data/Bivin CC 2013-14_updated_headings.csv")
dim(df_17_19)[1] 165808 32[1] 114305 32[1] 95302 32#format date column
df_17_19$date = date.mmddyy(mdy.date(match(substr(df_17_19$Month, 1, 3),month.abb),01,df_17_19$Year),sep="/")
df_15_16$date = date.mmddyy(mdy.date(match(substr(df_15_16$Month, 4, 6),month.abb),01,df_15_16$Year),sep="/")
df_13_14$date = date.mmddyy(mdy.date(match(substr(df_13_14$Month, 1, 3),month.abb),01,df_13_14$Year),sep="/")
df <- rbind(df_17_19,df_15_16,df_13_14)
dim(df)[1] 375415 33Check for Missing Data
Here we create a function to check for missing data.
check.for.missing.data <- function(data){
a = colnames(data)
b = colSums(is.na(df)) %>% as.data.table
missing_value_table = cbind(a, b)
colnames(missing_value_table) = c("Variables","Missing_values")
missing_value_table = missing_value_table %>% filter(Missing_values>0) %>%
mutate("As a % of Total Values" = round(100 * (Missing_values / nrow(df)), 1)) %>%
arrange(desc(Missing_values))
head(missing_value_table, 20)
}
table_a = check.for.missing.data(data=df)
# display table with first column aligned left all others aligned right
formattable(table_a, align = c("l", rep("r", NCOL(table_a) - 1)))| Variables | Missing_values | As a % of Total Values |
|---|---|---|
| Metrics | 375415 | 100 |
Drop Variables
drops <- c("Metrics","Year","Month","House","Account_Status","Beverage_Type","Fiscal_Year","Premise","Customer_Street_Address","Customer_City",
"Customer_Zip_Code","Longitude_Customer","Latitude_Customer","Customer","Vendor","Brand_ID","Brand","Size","Product_ID","Chain","Category",
"Product_Type_ID","Qty_Per_Case","Alcohol_Proof","X9L_Cases","Dollar_Sales_Per_Case","Dollar_Sales_Per_9L_Case")
df = df[ , !(names(df) %in% drops)]Variable Formatting
'data.frame': 375415 obs. of 6 variables:
$ Customer_ID : int 701000317 701001770 701000317 701001770 701000317 701000317 701001770 701001770 701001770 701001770 ...
$ Product : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 1211 2325 2325 2325 1972 1211 2325 2325 2325 ...
$ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 29 49 49 49 54 29 49 49 49 ...
$ STD_Cases : num 377 361 330 307 280 231 217 192 192 190 ...
$ Dollar_Sales: num 21987 69846 19246 17904 16498 ...
$ date : chr "3/1/2017" "3/1/2018" "3/1/2018" "3/1/2018" ...Products
[1] 57 2| Product_Type | n |
|---|---|
| FLAVORED | 69425 |
| VODKA | 48349 |
| WHISKEY | 33177 |
| BOURBON | 18838 |
| BLENDS | 18737 |
| SILVER | 18317 |
[1] 4017 2| Product | n |
|---|---|
| TAAKA VODKA 80 PET 1.75L | 2385 |
| JACK DANIELS BLK WHSKY 1L | 2269 |
| TAAKA VODKA 80 1L | 2183 |
| CLAN MCGREGOR SCOTCH 1.75L | 2091 |
| RICH & RARE CANADIAN WHSKY 1.75L | 2068 |
| JACK DANIELS BLK WHSKY 1.75L | 1994 |
[1] 34 2| Customer_ID | n |
|---|---|
| 700005448 | 37041 |
| 701001810 | 21316 |
| 701001907 | 19528 |
| 701001904 | 17879 |
| 701000317 | 17043 |
| 701001770 | 15558 |
product_type_product_group = df %>% group_by(Product_Type, Product) %>% tally(sort=TRUE)
dim(product_type_product_group)[1] 4017 3| Product_Type | Product | n |
|---|---|---|
| VODKA | TAAKA VODKA 80 PET 1.75L | 2385 |
| WHISKEY | JACK DANIELS BLK WHSKY 1L | 2269 |
| VODKA | TAAKA VODKA 80 1L | 2183 |
| SCOTCH | CLAN MCGREGOR SCOTCH 1.75L | 2091 |
| BLENDS | RICH & RARE CANADIAN WHSKY 1.75L | 2068 |
| WHISKEY | JACK DANIELS BLK WHSKY 1.75L | 1994 |
[1] 37391 4| Product_Type | Product | Customer_ID | n |
|---|---|---|---|
| BLENDS | CARSTAIRS BLEND 80 1L | 700005925 | 84 |
| BLENDS | CARSTAIRS BLEND 80 1L | 701000317 | 84 |
| BLENDS | CARSTAIRS BLEND 80 1L | 701001790 | 84 |
| BLENDS | RICH & RARE CANADIAN WHSKY 1.75L | 700005448 | 84 |
| BLENDS | RICH & RARE CANADIAN WHSKY 1.75L | 700005850 | 84 |
| BLENDS | RICH & RARE CANADIAN WHSKY 1.75L | 700005861 | 84 |
Put Combinations for Forecasting into a Dataframe and Choose 10 Sample Combinations
# Create file with all possible combinations
combinations0 = as.data.frame(df %>% group_by(Product_Type, Product, Customer_ID) %>% tally(sort=TRUE))
combinations = combinations0 %>% filter(n >= 42)
# Sample combinations
set.seed(123)
sample_combinations = sample_n(combinations,10)
drops <- c("n")
sample_combinations = sample_combinations[ , !(names(sample_combinations) %in% drops)]
formattable(sample_combinations, align = c("l", rep("r", NCOL(table_a) - 1)))| Product_Type | Product | Customer_ID |
|---|---|---|
| WHISKEY | JACK DANIELS BLK WHSKY 750M | 700005895 |
| SILVER | TORTILLA SILVER TEQ DSS 1.75L | 700005448 |
| GOLD | FLOR DE CANA GOLD RUM 4YR 1L | 701001904 |
| TEQUILA | CASA NOBLE CRYSTAL TEQ 6PK 750M | 700005925 |
| LIQUEUR | PIRAS 51 CACHACA 80 1L | 701001770 |
| VODKA | MCCORMICK VODKA 80 1.75L | 701001908 |
| VODKA | MCCORMICK VODKA 80 TRVL 750M | 700005926 |
| BLENDS | RICH & RARE CANADIAN RSV 6PK 750M | 701001850 |
| SILVER | 1800 SILVER TEQ 750M | 700005900 |
| FLAVORED | FIREBALL CINN WHSKY NL 1.75L | 701001907 |
Time Series EDA & Forecasting
# Find data from file for first combination
all_dates = data.frame(date=c("1/1/2013","2/1/2013","3/1/2013","4/1/2013","5/1/2013","6/1/2013","7/1/2013","8/1/2013","9/1/2013","10/1/2013","11/1/2013","12/1/2013",
"1/1/2014","2/1/2014","3/1/2014","4/1/2014","5/1/2014","6/1/2014","7/1/2014","8/1/2014","9/1/2014","10/1/2014","11/1/2014","12/1/2014",
"1/1/2015","2/1/2015","3/1/2015","4/1/2015","5/1/2015","6/1/2015","7/1/2015","8/1/2015","9/1/2015","10/1/2015","11/1/2015","12/1/2015",
"1/1/2016","2/1/2016","3/1/2016","4/1/2016","5/1/2016","6/1/2016","7/1/2016","8/1/2016","9/1/2016","10/1/2016","11/1/2016","12/1/2016",
"1/1/2017","2/1/2017","3/1/2017","4/1/2017","5/1/2017","6/1/2017","7/1/2017","8/1/2017","9/1/2017","10/1/2017","11/1/2017","12/1/2017",
"1/1/2018","2/1/2018","3/1/2018","4/1/2018","5/1/2018","6/1/2018","7/1/2018","8/1/2018","9/1/2018","10/1/2018","11/1/2018","12/1/2018",
"1/1/2019","2/1/2019","3/1/2019","4/1/2019","5/1/2019","6/1/2019","7/1/2019","8/1/2019","9/1/2019","10/1/2019","11/1/2019","12/1/2019"))
date_combinations = merge(all_dates,sample_combinations,all=TRUE)
str(date_combinations)'data.frame': 840 obs. of 4 variables:
$ date : Factor w/ 84 levels "1/1/2013","1/1/2014",..: 1 29 36 43 50 57 64 71 78 8 ...
$ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 53 53 53 53 53 53 53 53 53 53 ...
$ Product : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 1144 1144 1144 1144 1144 1144 1144 1144 1144 1144 ...
$ Customer_ID : int 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 ...# Join date/sample combinations with primary dataset to review records
temp = left_join(date_combinations,df)
# Replace missing values for STD_Cases and Dollar_Sales with zeros since no cases were sold those months
temp[is.na(temp)] <- 0
str(temp)'data.frame': 840 obs. of 6 variables:
$ date : chr "1/1/2013" "2/1/2013" "3/1/2013" "4/1/2013" ...
$ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 53 53 53 53 53 53 53 53 53 53 ...
$ Product : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 1144 1144 1144 1144 1144 1144 1144 1144 1144 1144 ...
$ Customer_ID : int 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 ...
$ STD_Cases : num 3 0 1 5 0 0 0 4 0 0 ...
$ Dollar_Sales: num 582 0 206 970 0 0 0 814 0 0 ...results <- data.frame(Product_Type=integer(),
Product=character(),
Customer=integer(),
ljung_10=double(),
ljung_24=double(),
ljung_results=character(),
top_5_bic=character(),
ADF=double(),
PP=double(),
KPSS=double(),
stationarity_results=character(),
EqualMeans_1_ASE=double(),
EqualMeans_2_ASE=double(),
EqualMeans_3_ASE=double(),
EqualMeans_4_ASE=double(),
EqualMeans_5_ASE=double(),
EqualMeans_6_ASE=double(),
EqualMeans_7_ASE=double(),
EqualMeans_8_ASE=double(),
EqualMeans_9_ASE=double(),
EqualMeans_10_ASE=double(),
EqualMeans_11_ASE=double(),
EqualMeans_12_ASE=double(),
ARMA_1_ASE=double(),
ARMA_2_ASE=double(),
ARMA_3_ASE=double(),
ARMA_4_ASE=double(),
ARMA_5_ASE=double(),
ARMA_6_ASE=double(),
ARMA_7_ASE=double(),
ARMA_8_ASE=double(),
ARMA_9_ASE=double(),
ARMA_10_ASE=double(),
ARMA_11_ASE=double(),
ARMA_12_ASE=double(),
ARIMA_1_ASE=double(),
ARIMA_2_ASE=double(),
ARIMA_3_ASE=double(),
ARIMA_4_ASE=double(),
ARIMA_5_ASE=double(),
ARIMA_6_ASE=double(),
ARIMA_7_ASE=double(),
ARIMA_8_ASE=double(),
ARIMA_9_ASE=double(),
ARIMA_10_ASE=double(),
ARIMA_11_ASE=double(),
ARIMA_12_ASE=double(),
ARIMA_S12_1_ASE=double(),
ARIMA_S12_2_ASE=double(),
ARIMA_S12_3_ASE=double(),
ARIMA_S12_4_ASE=double(),
ARIMA_S12_5_ASE=double(),
ARIMA_S12_6_ASE=double(),
ARIMA_S12_7_ASE=double(),
ARIMA_S12_8_ASE=double(),
ARIMA_S12_9_ASE=double(),
ARIMA_S12_10_ASE=double(),
ARIMA_S12_11_ASE=double(),
ARIMA_S12_12_ASE=double(),
stringsAsFactors = FALSE)
# loop through sample combinations
for(i in 1:10) {
sample_combinations1 = sample_combinations[i,]
temp1 = inner_join(temp,sample_combinations1)
product = sample_combinations1$Product
customer = sample_combinations1$Customer_ID
product_type = sample_combinations1$Customer_ID
results[i,"Product_Type"] = product_type
results[i,"Product"] = as.character(sample_combinations1$Product)
results[i,"Customer"] = customer
par(mfrow=c(1,1))
plot.ts(temp1$STD_Cases,
main=c(paste("Standard Case Sales of ", product),
paste("for Customer",customer)),
xlab="Months",
ylab="Standard Cases")
par(mfrow = c(2,2))
invisible(acf(temp1$STD_Cases, main="ACF"))
invisible(parzen.wge(temp1$STD_Cases))
invisible(acf(temp1$STD_Cases[0:length(temp1$date)/2], main="ACF for 1st Half of Series"))
invisible(acf(temp1$STD_Cases[(1+length(temp1$date)/2):length(temp1$date)], main="ACF for 2nd Half of Series"))
sink("file")
ljung_10 = ljung.wge(temp1$STD_Cases,K=10)
sink()
cat("The Ljung-Box test with K=10 has a p-value of",ljung_10$pval,".")
results[i,"ljung_10"] = ljung_10$pval
sink("file")
ljung_24 = ljung.wge(temp1$STD_Cases,K=24)
sink()
cat("The Ljung-Box test with K=24 has a p-value of",ljung_24$pval,".")
results[i,"ljung_24"] = ljung_24$pval
if (ljung_10$pval < .05 & ljung_24$pval < .05){
print("Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise.")
results[i,"ljung_results"] = "not white noise"
} else if (ljung_10$pval > .05 & ljung_24$pval < .05){
print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
results[i,"ljung_results"] = "inconclusive"
} else if (ljung_10$pval < .05 & ljung_24$pval > .05){
print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
results[i,"ljung_results"] = "inconclusive"
} else {
print("Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise.")
results[i,"ljung_results"] = "white noise"
}
sink("file")
aic = invisible(aic5.wge(temp1$STD_Cases,type="bic"))
sink()
for (row in 1:nrow(aic)) {
if(aic[row,1] == 0 & aic[row,2] == 0){
print("One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise.")
results[i,"top_5_bic"] = "white noise"
}
}
# Tests for stationarity
# Augmented Dickey-Fuller
adf=tseries::adf.test(temp1$STD_Cases)
results[i,"ADF"] = adf$p.value
# Phillips-Perron
pp=tseries::pp.test(temp1$STD_Cases)
results[i,"PP"] = pp$p.value
# Kwiatkowski-Phillips-Schmidt-Shin
kpss=tseries::kpss.test(temp1$STD_Cases)
results[i,"KPSS"] = kpss$p.value
if (adf$p.value < .05 & kpss$p.value > .05){
print("Both stationarity tests indicate this time series is stationary.")
results[i,"stationarity_results"] = "stationary"
} else if (adf$p.value >= .05 & kpss$p.value <= .05){
print("Both stationarity tests indicate this time series is NOT stationary.")
results[i,"stationarity_results"] = "not stationary"
} else {
print("Both tests for stationarity were inconclusive.")
results[i,"stationarity_results"] = "inconclusive"
}
j=12
#Equal Means Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
sink()
assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
results[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
results[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
results[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
results[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
results[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
results[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
results[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
results[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
results[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
results[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
results[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
#ARMA Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],type="aic"))
model1_est = invisible(est.arma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 0,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("ARMA_1_ASE")] = WindowedASE1
results[i,paste0("ARMA_2_ASE")] = WindowedASE2
results[i,paste0("ARMA_3_ASE")] = WindowedASE3
results[i,paste0("ARMA_4_ASE")] = WindowedASE4
results[i,paste0("ARMA_5_ASE")] = WindowedASE5
results[i,paste0("ARMA_6_ASE")] = WindowedASE6
results[i,paste0("ARMA_7_ASE")] = WindowedASE7
results[i,paste0("ARMA_8_ASE")] = WindowedASE8
results[i,paste0("ARMA_9_ASE")] = WindowedASE9
results[i,paste0("ARMA_10_ASE")] = WindowedASE10
results[i,paste0("ARMA_11_ASE")] = WindowedASE11
results[i,paste0("ARMA_12_ASE")] = WindowedASE12
#ARIMA Model with d=1
nulldev()
temp2 = artrans.wge(temp1$STD_Cases,1)
dev.off()
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],type="aic"))
model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 1,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARIMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("ARIMA_1_ASE")] = WindowedASE1
results[i,paste0("ARIMA_2_ASE")] = WindowedASE2
results[i,paste0("ARIMA_3_ASE")] = WindowedASE3
results[i,paste0("ARIMA_4_ASE")] = WindowedASE4
results[i,paste0("ARIMA_5_ASE")] = WindowedASE5
results[i,paste0("ARIMA_6_ASE")] = WindowedASE6
results[i,paste0("ARIMA_7_ASE")] = WindowedASE7
results[i,paste0("ARIMA_8_ASE")] = WindowedASE8
results[i,paste0("ARIMA_9_ASE")] = WindowedASE9
results[i,paste0("ARIMA_10_ASE")] = WindowedASE10
results[i,paste0("ARIMA_11_ASE")] = WindowedASE11
results[i,paste0("ARIMA_12_ASE")] = WindowedASE12
#ARIMA Model with S=12
nulldev()
temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
dev.off()
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],type="aic"))
model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-12))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 12, d = 0,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARIMAS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("ARIMA_S12_1_ASE")] = WindowedASE1
results[i,paste0("ARIMA_S12_2_ASE")] = WindowedASE2
results[i,paste0("ARIMA_S12_3_ASE")] = WindowedASE3
results[i,paste0("ARIMA_S12_4_ASE")] = WindowedASE4
results[i,paste0("ARIMA_S12_5_ASE")] = WindowedASE5
results[i,paste0("ARIMA_S12_6_ASE")] = WindowedASE6
results[i,paste0("ARIMA_S12_7_ASE")] = WindowedASE7
results[i,paste0("ARIMA_S12_8_ASE")] = WindowedASE8
results[i,paste0("ARIMA_S12_9_ASE")] = WindowedASE9
results[i,paste0("ARIMA_S12_10_ASE")] = WindowedASE10
results[i,paste0("ARIMA_S12_11_ASE")] = WindowedASE11
results[i,paste0("ARIMA_S12_12_ASE")] = WindowedASE12
#graph ASEs for each Model
EqualMeans_Results <- rbind(EqualMeans_Results_1,EqualMeans_Results_2,EqualMeans_Results_3,EqualMeans_Results_4,EqualMeans_Results_5,EqualMeans_Results_6,
EqualMeans_Results_7,EqualMeans_Results_8,EqualMeans_Results_9,EqualMeans_Results_10,EqualMeans_Results_11,EqualMeans_Results_12,
EqualMeans_Results_13)
ARMA_Results <- rbind(ARMA_Results_1,ARMA_Results_2,ARMA_Results_3,ARMA_Results_4,ARMA_Results_5,ARMA_Results_6,ARMA_Results_7,ARMA_Results_8,
ARMA_Results_9,ARMA_Results_10,ARMA_Results_11,ARMA_Results_12,ARMA_Results_13)
ARIMA_Results <- rbind(ARIMA_Results_1,ARIMA_Results_2,ARIMA_Results_3,ARIMA_Results_4,ARIMA_Results_5,ARIMA_Results_6,ARIMA_Results_7,ARIMA_Results_8,
ARIMA_Results_9,ARIMA_Results_10,ARIMA_Results_11,ARIMA_Results_12,ARIMA_Results_13)
ARIMAS_Results <- rbind(ARIMAS_Results_1,ARIMAS_Results_2,ARIMAS_Results_3,ARIMAS_Results_4,ARIMAS_Results_5,ARIMAS_Results_6,ARIMAS_Results_7,ARIMAS_Results_8,
ARIMAS_Results_9,ARIMAS_Results_10,ARIMAS_Results_11,ARIMAS_Results_12,ARIMAS_Results_13)
EqualMeans_Means <- colMeans(EqualMeans_Results)
ARMA_Means <- colMeans(ARMA_Results)
ARIMA_Means <- colMeans(ARIMA_Results)
ARIMAS_Means <- colMeans(ARIMAS_Results)
Combined_Means <- data.frame(EqualMeans_Means,ARMA_Means, ARIMA_Means, ARIMAS_Means)
Combined_Means$horizon <- as.numeric(row.names(Combined_Means))
g <- ggplot(data=Combined_Means, aes(horizon)) +
geom_line(aes(y=EqualMeans_Means, color="Equal Means"),size=1.5) +
geom_line(aes(y=ARMA_Means, color="ARMA"),size=1.5) +
geom_line(aes(y=ARIMA_Means, color="ARIMA"),size=1.5) +
geom_line(aes(y=ARIMAS_Means, color="ARIMAS"),size=1.5) +
scale_color_manual(values = c(
'Equal Means' = '#58508d',
'ARMA' = '#bc5090',
'ARIMA' = '#ff6361',
'ARIMAS' = '#ffa600'
)) +
labs(color='Models') +
scale_x_continuous(breaks=seq(0,13,1)) +
ggtitle(paste("Model ASEs for ", product,"and Customer",customer)) +
xlab("Month Ahead Forecast") +
ylab("ASE") +
theme(panel.background = element_blank(), axis.line = element_line(colour = "black"), legend.title = element_blank())
print(g)
}
The Ljung-Box test with K=10 has a p-value of 4.786171e-12 .The Ljung-Box test with K=24 has a p-value of 1.665335e-15 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.08807377 .The Ljung-Box test with K=24 has a p-value of 0.3665865 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.3801776 .The Ljung-Box test with K=24 has a p-value of 0.1126704 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.0009489966 .The Ljung-Box test with K=24 has a p-value of 0.0002502709 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.0186233 .The Ljung-Box test with K=24 has a p-value of 0.005561031 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 6.426664e-08 .The Ljung-Box test with K=24 has a p-value of 6.568032e-10 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 2.934075e-10 .The Ljung-Box test with K=24 has a p-value of 3.874856e-11 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.6360152 .The Ljung-Box test with K=24 has a p-value of 0.844331 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."
The Ljung-Box test with K=10 has a p-value of 0.06656046 .The Ljung-Box test with K=24 has a p-value of 0.0002436308 .[1] "Ljung-Box test results: At a significance level of 0.05, the test is inconclusive."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.02684747 .The Ljung-Box test with K=24 has a p-value of 0.00508631 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
| Product_Type | Product | Customer | ljung_10 | ljung_24 | ljung_results | top_5_bic | ADF | PP | KPSS | stationarity_results | EqualMeans_1_ASE | EqualMeans_2_ASE | EqualMeans_3_ASE | EqualMeans_4_ASE | EqualMeans_5_ASE | EqualMeans_6_ASE | EqualMeans_7_ASE | EqualMeans_8_ASE | EqualMeans_9_ASE | EqualMeans_10_ASE | EqualMeans_11_ASE | EqualMeans_12_ASE | ARMA_1_ASE | ARMA_2_ASE | ARMA_3_ASE | ARMA_4_ASE | ARMA_5_ASE | ARMA_6_ASE | ARMA_7_ASE | ARMA_8_ASE | ARMA_9_ASE | ARMA_10_ASE | ARMA_11_ASE | ARMA_12_ASE | ARIMA_1_ASE | ARIMA_2_ASE | ARIMA_3_ASE | ARIMA_4_ASE | ARIMA_5_ASE | ARIMA_6_ASE | ARIMA_7_ASE | ARIMA_8_ASE | ARIMA_9_ASE | ARIMA_10_ASE | ARIMA_11_ASE | ARIMA_12_ASE | ARIMA_S12_1_ASE | ARIMA_S12_2_ASE | ARIMA_S12_3_ASE | ARIMA_S12_4_ASE | ARIMA_S12_5_ASE | ARIMA_S12_6_ASE | ARIMA_S12_7_ASE | ARIMA_S12_8_ASE | ARIMA_S12_9_ASE | ARIMA_S12_10_ASE | ARIMA_S12_11_ASE | ARIMA_S12_12_ASE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 700005895 | JACK DANIELS BLK WHSKY 750M | 700005895 | 4.786171e-12 | 1.665335e-15 | not white noise | NA | 0.01000000 | 0.01 | 0.01000000 | inconclusive | 9.0689744 | 9.1510256 | 9.1886325 | 9.1215385 | 9.2110256 | 9.6625641 | 9.9165934 | 10.1410897 | 10.2612821 | 10.3625641 | 10.2468298 | 10.6138462 | 5.5392257 | 5.9681069 | 6.3616927 | 6.4042988 | 6.4227636 | 6.4027409 | 6.6372491 | 6.7007490 | 6.7862477 | 6.7964345 | 6.7325565 | 6.8699152 | 8.5418681 | 9.2801912 | 8.6697046 | 9.3972474 | 9.5739507 | 9.0672141 | 9.6068875 | 9.4353998 | 9.5065170 | 9.6750977 | 9.3342680 | 9.3124904 | 9.155954 | 9.981319 | 10.046597 | 10.254467 | 10.473186 | 10.450372 | 10.530208 | 10.474697 | 10.512969 | 10.469637 | 10.440687 | 9.977978 |
| 700005448 | TORTILLA SILVER TEQ DSS 1.75L | 700005448 | 8.807377e-02 | 3.665865e-01 | white noise | white noise | 0.36870575 | 0.01 | 0.04762877 | not stationary | 0.5716556 | 0.5655017 | 0.5624248 | 0.5890915 | 0.6004761 | 0.6090060 | 0.6144394 | 0.6163350 | 0.6305729 | 0.6623222 | 0.6920285 | 0.7245188 | 0.7207688 | 0.6861532 | 0.6757951 | 0.6679848 | 0.6538848 | 0.6548755 | 0.6565445 | 0.6579988 | 0.6676573 | 0.6958380 | 0.7219311 | 0.7529246 | 0.6405925 | 0.6299260 | 0.6164646 | 0.6233314 | 0.6240543 | 0.6366802 | 0.6364920 | 0.6307053 | 0.6530211 | 0.6699885 | 0.6931830 | 0.7184782 | 2.032046 | 1.722801 | 1.651667 | 1.800139 | 2.099372 | 2.177397 | 2.211459 | 2.195750 | 2.284632 | 2.260631 | 2.206559 | 2.181600 |
| 701001904 | FLOR DE CANA GOLD RUM 4YR 1L | 701001904 | 3.801776e-01 | 1.126704e-01 | white noise | white noise | 0.01799216 | 0.01 | 0.01000000 | inconclusive | 0.6995513 | 0.5290385 | 0.4687821 | 0.4425000 | 0.4523718 | 0.4589530 | 0.4816026 | 0.5017949 | 0.5197792 | 0.5367308 | 0.5501340 | 0.5606624 | 1.0442915 | 0.8301104 | 0.7067074 | 0.6343535 | 0.6128546 | 0.5994945 | 0.5999598 | 0.6006017 | 0.6010513 | 0.6102566 | 0.6137591 | 0.6163443 | 1.9471137 | 1.3335527 | 1.1635218 | 1.0611714 | 1.0070012 | 1.0167857 | 0.9846006 | 1.0169535 | 1.0343591 | 1.0306570 | 1.0266886 | 1.0104301 | 1.772864 | 2.322617 | 2.302087 | 2.249213 | 2.201378 | 2.157702 | 2.153409 | 2.092362 | 2.041340 | 2.006400 | 1.978361 | 1.954473 |
| 700005925 | CASA NOBLE CRYSTAL TEQ 6PK 750M | 700005925 | 9.489966e-04 | 2.502709e-04 | not white noise | white noise | 0.56183917 | 0.01 | 0.10000000 | inconclusive | 3.1726068 | 3.2405556 | 2.7649145 | 2.5264530 | 2.3567094 | 2.2431197 | 2.1619841 | 2.0844658 | 2.0233191 | 1.9738889 | 1.9341453 | 1.8899145 | 4.6180807 | 4.3620508 | 3.4623764 | 3.1590933 | 2.8408239 | 2.6484569 | 2.5365775 | 2.3976202 | 2.3051311 | 2.2344015 | 2.1656202 | 2.1016788 | 5.7705099 | 5.0332742 | 4.0433952 | 3.6224390 | 3.1748973 | 3.0480544 | 2.8517410 | 2.6583122 | 2.6026693 | 2.4718678 | 2.3973343 | 2.3338023 | 6.311784 | 7.842069 | 8.196566 | 8.260550 | 8.124630 | 8.058478 | 7.944359 | 7.942456 | 7.808970 | 7.577955 | 7.185047 | 6.843732 |
| 701001770 | PIRAS 51 CACHACA 80 1L | 701001770 | 1.862330e-02 | 5.561031e-03 | not white noise | white noise | 0.21808191 | 0.01 | 0.07405623 | inconclusive | 0.7631624 | 0.7772650 | 0.7768376 | 0.7029060 | 0.6354701 | 0.6046154 | 0.6243346 | 0.6400855 | 0.6620228 | 0.6680342 | 0.6624631 | 0.6627350 | 0.6446346 | 0.6657276 | 0.6525417 | 0.5925254 | 0.5308812 | 0.5020173 | 0.5298103 | 0.5568825 | 0.5879643 | 0.6020638 | 0.6045947 | 0.6120855 | 0.5001610 | 0.5698775 | 0.6161735 | 0.6000020 | 0.5748791 | 0.5755548 | 0.6115162 | 0.6488012 | 0.6920893 | 0.7273038 | 0.7643915 | 0.7972260 | 2.133433 | 2.262730 | 2.385876 | 2.528330 | 2.554339 | 2.586967 | 2.650574 | 2.684445 | 2.731844 | 2.739532 | 2.727685 | 2.665071 |
| 701001908 | MCCORMICK VODKA 80 1.75L | 701001908 | 6.426664e-08 | 6.568032e-10 | not white noise | NA | 0.35666834 | 0.01 | 0.01740497 | not stationary | 2.2285256 | 2.4682692 | 2.0174145 | 1.8387821 | 1.7351923 | 1.6960470 | 1.6831044 | 1.6737179 | 1.6755342 | 1.6782692 | 1.6840035 | 1.6919872 | 2.6388001 | 2.9401760 | 2.8495561 | 2.5864904 | 2.3975025 | 2.3198086 | 2.2665143 | 2.2897757 | 2.3101477 | 2.2679359 | 2.1984358 | 2.1269990 | 2.8193328 | 3.1843995 | 3.1282574 | 3.0207945 | 2.9848679 | 3.0366704 | 2.9866854 | 2.8984773 | 2.8083638 | 2.6253766 | 2.4693641 | 2.3587800 | 2.718075 | 2.731890 | 2.603679 | 2.389337 | 2.253288 | 2.245274 | 2.215078 | 2.217877 | 2.233337 | 2.231591 | 2.235785 | 2.232764 |
| 700005926 | MCCORMICK VODKA 80 TRVL 750M | 700005926 | 2.934075e-10 | 3.874856e-11 | not white noise | NA | 0.07556121 | 0.01 | 0.10000000 | inconclusive | 0.6716239 | 0.5062393 | 0.4528205 | 0.4171368 | 0.3767521 | 0.3481197 | 0.3262027 | 0.3161752 | 0.3018234 | 0.2911111 | 0.2919037 | 0.2927778 | 0.5968163 | 0.4579625 | 0.4497181 | 0.4511265 | 0.4286348 | 0.4049576 | 0.3825204 | 0.3637018 | 0.3428458 | 0.3270631 | 0.3227980 | 0.3181758 | 0.7227470 | 0.5716485 | 0.6012171 | 0.6667377 | 0.7006763 | 0.6931936 | 0.7031823 | 0.7046800 | 0.6948582 | 0.6932306 | 0.6941748 | 0.6899631 | 2.242084 | 1.956935 | 2.049454 | 1.863884 | 1.727736 | 1.549117 | 1.558636 | 1.507911 | 1.542104 | 1.495994 | 1.398345 | 1.408520 |
| 701001850 | RICH & RARE CANADIAN RSV 6PK 750M | 701001850 | 6.360152e-01 | 8.443310e-01 | white noise | white noise | 0.03437467 | 0.01 | 0.10000000 | stationary | 11.9384353 | 10.4039481 | 9.9608284 | 10.6224737 | 10.8606404 | 11.0467686 | 11.1601569 | 11.2330186 | 11.2435663 | 11.3251840 | 11.5126614 | 11.6416917 | 10.9581620 | 10.7792516 | 11.0698208 | 12.0680550 | 12.0926064 | 12.3485626 | 12.1985500 | 12.0879789 | 12.0085145 | 12.0304265 | 12.1421225 | 12.2456236 | 15.9706679 | 14.2314006 | 12.0051347 | 14.2947521 | 14.6930887 | 14.8401812 | 14.7715397 | 15.1490428 | 14.9630577 | 15.3793237 | 15.4024611 | 15.4003271 | 15.974995 | 19.457766 | 19.705139 | 19.398040 | 17.880262 | 17.076971 | 16.550790 | 16.126107 | 15.784831 | 15.735607 | 15.589212 | 15.317253 |
| 700005900 | 1800 SILVER TEQ 750M | 700005900 | 6.656046e-02 | 2.436308e-04 | inconclusive | white noise | 0.01000000 | 0.01 | 0.01000000 | inconclusive | 1.1171368 | 1.1107265 | 1.1102991 | 1.1081624 | 1.1017521 | 1.1201282 | 1.0706166 | 1.0338034 | 1.0060256 | 0.9840598 | 0.9670202 | 0.9756838 | 1.3180946 | 1.2112054 | 1.1772851 | 1.1584018 | 1.1419437 | 1.1536212 | 1.0993249 | 1.0589231 | 1.0283543 | 1.0041556 | 0.9852891 | 0.9924302 | 1.5081476 | 1.4503722 | 1.2940762 | 1.3000560 | 1.1782780 | 1.1161573 | 1.0581466 | 1.0076505 | 0.9827825 | 0.9540515 | 0.9299877 | 0.9175731 | 1.240651 | 1.421723 | 1.520543 | 1.556107 | 1.579133 | 1.557323 | 1.510084 | 1.475001 | 1.447865 | 1.426175 | 1.436418 | 1.425711 |
| 701001907 | FIREBALL CINN WHSKY NL 1.75L | 701001907 | 2.684747e-02 | 5.086310e-03 | not white noise | white noise | 0.04668965 | 0.01 | 0.01000000 | inconclusive | 3.4168803 | 3.3079060 | 2.9254274 | 2.7130342 | 2.5886752 | 2.5040598 | 2.4198107 | 2.3614316 | 2.3071937 | 2.2732906 | 2.2324981 | 2.2626068 | 3.7157148 | 3.4365654 | 3.1173311 | 2.9231418 | 2.8139887 | 2.7461842 | 2.6322659 | 2.5592011 | 2.4549392 | 2.3839704 | 2.3220255 | 2.3329799 | 5.8000703 | 5.1632613 | 4.7546005 | 4.5020618 | 4.4388272 | 4.0885904 | 3.9722412 | 3.9131948 | 3.7770898 | 3.7799643 | 3.7415046 | 3.8206163 | 3.409515 | 4.526630 | 5.475029 | 6.034526 | 5.773231 | 5.414569 | 5.320162 | 5.250294 | 5.147824 | 4.962384 | 4.771355 | 4.783543 |
Forecast Aggregation by Product
# Filter dataset to only 1 product
df_taaka = df[df$Product == "TAAKA VODKA 80 1L",]
combinations0 = as.data.frame(df_taaka %>% group_by(Product_Type, Product,Customer_ID) %>% tally(sort=TRUE))
combinations = combinations0 %>% filter(n >= 42)
combinations_mean = combinations0 %>% filter(n < 42)
# Find data from file for first combination
all_dates = data.frame(date=c("1/1/2013","2/1/2013","3/1/2013","4/1/2013","5/1/2013","6/1/2013","7/1/2013","8/1/2013","9/1/2013","10/1/2013","11/1/2013","12/1/2013",
"1/1/2014","2/1/2014","3/1/2014","4/1/2014","5/1/2014","6/1/2014","7/1/2014","8/1/2014","9/1/2014","10/1/2014","11/1/2014","12/1/2014",
"1/1/2015","2/1/2015","3/1/2015","4/1/2015","5/1/2015","6/1/2015","7/1/2015","8/1/2015","9/1/2015","10/1/2015","11/1/2015","12/1/2015",
"1/1/2016","2/1/2016","3/1/2016","4/1/2016","5/1/2016","6/1/2016","7/1/2016","8/1/2016","9/1/2016","10/1/2016","11/1/2016","12/1/2016",
"1/1/2017","2/1/2017","3/1/2017","4/1/2017","5/1/2017","6/1/2017","7/1/2017","8/1/2017","9/1/2017","10/1/2017","11/1/2017","12/1/2017",
"1/1/2018","2/1/2018","3/1/2018","4/1/2018","5/1/2018","6/1/2018","7/1/2018","8/1/2018","9/1/2018","10/1/2018","11/1/2018","12/1/2018",
"1/1/2019","2/1/2019","3/1/2019","4/1/2019","5/1/2019","6/1/2019","7/1/2019","8/1/2019","9/1/2019","10/1/2019","11/1/2019","12/1/2019"))
date_combinations = merge(all_dates,combinations,all=TRUE)
date_combinations_mean = merge(all_dates,combinations_mean,all=TRUE)
str(date_combinations)'data.frame': 2436 obs. of 5 variables:
$ date : Factor w/ 84 levels "1/1/2013","1/1/2014",..: 1 29 36 43 50 57 64 71 78 8 ...
$ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 49 49 49 49 49 49 49 49 49 ...
$ Product : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 2325 2325 2325 2325 2325 2325 2325 2325 2325 ...
$ Customer_ID : int 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 ...
$ n : int 84 84 84 84 84 84 84 84 84 84 ...# Join date/sample combinations with primary dataset to review records
temp = left_join(date_combinations,df_taaka)
temp_mean = left_join(date_combinations_mean,df_taaka)
# Replace missing values for STD_Cases and Dollar_Sales with zeros since no cases were sold those months
temp[is.na(temp)] <- 0
str(temp)'data.frame': 2436 obs. of 7 variables:
$ date : chr "1/1/2013" "2/1/2013" "3/1/2013" "4/1/2013" ...
$ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 49 49 49 49 49 49 49 49 49 ...
$ Product : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 2325 2325 2325 2325 2325 2325 2325 2325 2325 ...
$ Customer_ID : int 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 ...
$ n : int 84 84 84 84 84 84 84 84 84 84 ...
$ STD_Cases : num 53.8 58 67 68 72 66 72 72 44 49.8 ...
$ Dollar_Sales: num 3135 3379 3903 3961 4194 ...'data.frame': 336 obs. of 7 variables:
$ date : chr "1/1/2013" "2/1/2013" "3/1/2013" "4/1/2013" ...
$ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 49 49 49 49 49 49 49 49 49 ...
$ Product : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 2325 2325 2325 2325 2325 2325 2325 2325 2325 ...
$ Customer_ID : int 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 ...
$ n : int 39 39 39 39 39 39 39 39 39 39 ...
$ STD_Cases : num 2 0 0 1 1 0 0 0 0 0 ...
$ Dollar_Sales: num 117 0 0 58 58 0 0 0 0 0 ...z = nrow(combinations)
results <- data.frame(Product_Type=integer(),
Product=character(),
Customer=integer(),
ljung_10=double(),
ljung_24=double(),
ljung_results=character(),
top_5_bic=character(),
ADF=double(),
PP=double(),
KPSS=double(),
stationarity_results=character(),
EqualMeans_1_ASE=double(),
EqualMeans_2_ASE=double(),
EqualMeans_3_ASE=double(),
EqualMeans_4_ASE=double(),
EqualMeans_5_ASE=double(),
EqualMeans_6_ASE=double(),
EqualMeans_7_ASE=double(),
EqualMeans_8_ASE=double(),
EqualMeans_9_ASE=double(),
EqualMeans_10_ASE=double(),
EqualMeans_11_ASE=double(),
EqualMeans_12_ASE=double(),
EqualMeans_F1=double(),
EqualMeans_F2=double(),
EqualMeans_F3=double(),
EqualMeans_F4=double(),
EqualMeans_F5=double(),
EqualMeans_F6=double(),
EqualMeans_F7=double(),
EqualMeans_F8=double(),
EqualMeans_F9=double(),
EqualMeans_F10=double(),
EqualMeans_F11=double(),
EqualMeans_F12=double(),
ARMA_1_ASE=double(),
ARMA_2_ASE=double(),
ARMA_3_ASE=double(),
ARMA_4_ASE=double(),
ARMA_5_ASE=double(),
ARMA_6_ASE=double(),
ARMA_7_ASE=double(),
ARMA_8_ASE=double(),
ARMA_9_ASE=double(),
ARMA_10_ASE=double(),
ARMA_11_ASE=double(),
ARMA_12_ASE=double(),
ARMA_F1=double(),
ARMA_F2=double(),
ARMA_F3=double(),
ARMA_F4=double(),
ARMA_F5=double(),
ARMA_F6=double(),
ARMA_F7=double(),
ARMA_F8=double(),
ARMA_F9=double(),
ARMA_F10=double(),
ARMA_F11=double(),
ARMA_F12=double(),
ARIMA_1_ASE=double(),
ARIMA_2_ASE=double(),
ARIMA_3_ASE=double(),
ARIMA_4_ASE=double(),
ARIMA_5_ASE=double(),
ARIMA_6_ASE=double(),
ARIMA_7_ASE=double(),
ARIMA_8_ASE=double(),
ARIMA_9_ASE=double(),
ARIMA_10_ASE=double(),
ARIMA_11_ASE=double(),
ARIMA_12_ASE=double(),
ARIMA_F1=double(),
ARIMA_F2=double(),
ARIMA_F3=double(),
ARIMA_F4=double(),
ARIMA_F5=double(),
ARIMA_F6=double(),
ARIMA_F7=double(),
ARIMA_F8=double(),
ARIMA_F9=double(),
ARIMA_F10=double(),
ARIMA_F11=double(),
ARIMA_F12=double(),
ARIMA_S12_1_ASE=double(),
ARIMA_S12_2_ASE=double(),
ARIMA_S12_3_ASE=double(),
ARIMA_S12_4_ASE=double(),
ARIMA_S12_5_ASE=double(),
ARIMA_S12_6_ASE=double(),
ARIMA_S12_7_ASE=double(),
ARIMA_S12_8_ASE=double(),
ARIMA_S12_9_ASE=double(),
ARIMA_S12_10_ASE=double(),
ARIMA_S12_11_ASE=double(),
ARIMA_S12_12_ASE=double(),
ARIMA_S12_F1=double(),
ARIMA_S12_F2=double(),
ARIMA_S12_F3=double(),
ARIMA_S12_F4=double(),
ARIMA_S12_F5=double(),
ARIMA_S12_F6=double(),
ARIMA_S12_F7=double(),
ARIMA_S12_F8=double(),
ARIMA_S12_F9=double(),
ARIMA_S12_F10=double(),
ARIMA_S12_F11=double(),
ARIMA_S12_F12=double(),
ACTUAL_1=double(),
ACTUAL_2=double(),
ACTUAL_3=double(),
ACTUAL_4=double(),
ACTUAL_5=double(),
ACTUAL_6=double(),
ACTUAL_7=double(),
ACTUAL_8=double(),
ACTUAL_9=double(),
ACTUAL_10=double(),
ACTUAL_11=double(),
ACTUAL_12=double(),
stringsAsFactors = FALSE)
# loop through sample combinations
for(i in 1:z) {
sample_combinations1 = combinations[i,]
temp1 = inner_join(temp,sample_combinations1)
product = sample_combinations1$Product
customer = sample_combinations1$Customer_ID
product_type = sample_combinations1$Customer_ID
results[i,"Product_Type"] = product_type
results[i,"Product"] = as.character(sample_combinations1$Product)
results[i,"Customer"] = customer
par(mfrow=c(1,1))
plot.ts(temp1$STD_Cases,
main=c(paste("Standard Case Sales of ", product),
paste("for Customer",customer)),
xlab="Months",
ylab="Standard Cases")
par(mfrow = c(2,2))
invisible(acf(temp1$STD_Cases, main="ACF"))
invisible(parzen.wge(temp1$STD_Cases))
invisible(acf(temp1$STD_Cases[0:length(temp1$date)/2], main="ACF for 1st Half of Series"))
invisible(acf(temp1$STD_Cases[(1+length(temp1$date)/2):length(temp1$date)], main="ACF for 2nd Half of Series"))
sink("file")
ljung_10 = ljung.wge(temp1$STD_Cases,K=10)
sink()
cat("The Ljung-Box test with K=10 has a p-value of",ljung_10$pval,".")
results[i,"ljung_10"] = ljung_10$pval
sink("file")
ljung_24 = ljung.wge(temp1$STD_Cases,K=24)
sink()
cat("The Ljung-Box test with K=24 has a p-value of",ljung_24$pval,".")
results[i,"ljung_24"] = ljung_24$pval
if (ljung_10$pval < .05 & ljung_24$pval < .05){
print("Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise.")
results[i,"ljung_results"] = "not white noise"
} else if (ljung_10$pval > .05 & ljung_24$pval < .05){
print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
results[i,"ljung_results"] = "inconclusive"
} else if (ljung_10$pval < .05 & ljung_24$pval > .05){
print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
results[i,"ljung_results"] = "inconclusive"
} else {
print("Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise.")
results[i,"ljung_results"] = "white noise"
}
sink("file")
aic = invisible(aic5.wge(temp1$STD_Cases,type="bic"))
sink()
for (row in 1:nrow(aic)) {
if(aic[row,1] == 0 & aic[row,2] == 0){
print("One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise.")
results[i,"top_5_bic"] = "white noise"
}
}
# Tests for stationarity
# Augmented Dickey-Fuller
adf=tseries::adf.test(temp1$STD_Cases)
results[i,"ADF"] = adf$p.value
# Phillips-Perron
pp=tseries::pp.test(temp1$STD_Cases)
results[i,"PP"] = pp$p.value
# Kwiatkowski-Phillips-Schmidt-Shin
kpss=tseries::kpss.test(temp1$STD_Cases)
results[i,"KPSS"] = kpss$p.value
if (adf$p.value < .05 & kpss$p.value > .05){
print("Both stationarity tests indicate this time series is stationary.")
results[i,"stationarity_results"] = "stationary"
} else if (adf$p.value >= .05 & kpss$p.value <= .05){
print("Both stationarity tests indicate this time series is NOT stationary.")
results[i,"stationarity_results"] = "not stationary"
} else {
print("Both tests for stationarity were inconclusive.")
results[i,"stationarity_results"] = "inconclusive"
}
j=12
#Equal Means Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
sink()
assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
results[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
results[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
results[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
results[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
results[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
results[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
results[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
results[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
results[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
results[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
results[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
results[i,paste0("EqualMeans_F1")] = model0_mean
results[i,paste0("EqualMeans_F2")] = model0_mean
results[i,paste0("EqualMeans_F3")] = model0_mean
results[i,paste0("EqualMeans_F4")] = model0_mean
results[i,paste0("EqualMeans_F5")] = model0_mean
results[i,paste0("EqualMeans_F6")] = model0_mean
results[i,paste0("EqualMeans_F7")] = model0_mean
results[i,paste0("EqualMeans_F8")] = model0_mean
results[i,paste0("EqualMeans_F9")] = model0_mean
results[i,paste0("EqualMeans_F10")] = model0_mean
results[i,paste0("EqualMeans_F11")] = model0_mean
results[i,paste0("EqualMeans_F12")] = model0_mean
#ARMA Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],type="aic"))
model1_est = invisible(est.arma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 0,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("ARMA_1_ASE")] = WindowedASE1
results[i,paste0("ARMA_2_ASE")] = WindowedASE2
results[i,paste0("ARMA_3_ASE")] = WindowedASE3
results[i,paste0("ARMA_4_ASE")] = WindowedASE4
results[i,paste0("ARMA_5_ASE")] = WindowedASE5
results[i,paste0("ARMA_6_ASE")] = WindowedASE6
results[i,paste0("ARMA_7_ASE")] = WindowedASE7
results[i,paste0("ARMA_8_ASE")] = WindowedASE8
results[i,paste0("ARMA_9_ASE")] = WindowedASE9
results[i,paste0("ARMA_10_ASE")] = WindowedASE10
results[i,paste0("ARMA_11_ASE")] = WindowedASE11
results[i,paste0("ARMA_12_ASE")] = WindowedASE12
results[i,paste0("ARMA_F1")] = forecasts$f[1]
results[i,paste0("ARMA_F2")] = forecasts$f[2]
results[i,paste0("ARMA_F3")] = forecasts$f[3]
results[i,paste0("ARMA_F4")] = forecasts$f[4]
results[i,paste0("ARMA_F5")] = forecasts$f[5]
results[i,paste0("ARMA_F6")] = forecasts$f[6]
results[i,paste0("ARMA_F7")] = forecasts$f[7]
results[i,paste0("ARMA_F8")] = forecasts$f[8]
results[i,paste0("ARMA_F9")] = forecasts$f[9]
results[i,paste0("ARMA_F10")] = forecasts$f[10]
results[i,paste0("ARMA_F11")] = forecasts$f[11]
results[i,paste0("ARMA_F12")] = forecasts$f[12]
#ARIMA Model with d=1
nulldev()
temp2 = artrans.wge(temp1$STD_Cases,1)
dev.off()
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],type="aic"))
model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 1,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARIMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("ARIMA_1_ASE")] = WindowedASE1
results[i,paste0("ARIMA_2_ASE")] = WindowedASE2
results[i,paste0("ARIMA_3_ASE")] = WindowedASE3
results[i,paste0("ARIMA_4_ASE")] = WindowedASE4
results[i,paste0("ARIMA_5_ASE")] = WindowedASE5
results[i,paste0("ARIMA_6_ASE")] = WindowedASE6
results[i,paste0("ARIMA_7_ASE")] = WindowedASE7
results[i,paste0("ARIMA_8_ASE")] = WindowedASE8
results[i,paste0("ARIMA_9_ASE")] = WindowedASE9
results[i,paste0("ARIMA_10_ASE")] = WindowedASE10
results[i,paste0("ARIMA_11_ASE")] = WindowedASE11
results[i,paste0("ARIMA_12_ASE")] = WindowedASE12
results[i,paste0("ARIMA_F1")] = forecasts$f[1]
results[i,paste0("ARIMA_F2")] = forecasts$f[2]
results[i,paste0("ARIMA_F3")] = forecasts$f[3]
results[i,paste0("ARIMA_F4")] = forecasts$f[4]
results[i,paste0("ARIMA_F5")] = forecasts$f[5]
results[i,paste0("ARIMA_F6")] = forecasts$f[6]
results[i,paste0("ARIMA_F7")] = forecasts$f[7]
results[i,paste0("ARIMA_F8")] = forecasts$f[8]
results[i,paste0("ARIMA_F9")] = forecasts$f[9]
results[i,paste0("ARIMA_F10")] = forecasts$f[10]
results[i,paste0("ARIMA_F11")] = forecasts$f[11]
results[i,paste0("ARIMA_F12")] = forecasts$f[12]
#ARIMA Model with S=12
nulldev()
temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
dev.off()
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],type="aic"))
model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-12))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 12, d = 0,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARIMAS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results[i,paste0("ARIMA_S12_1_ASE")] = WindowedASE1
results[i,paste0("ARIMA_S12_2_ASE")] = WindowedASE2
results[i,paste0("ARIMA_S12_3_ASE")] = WindowedASE3
results[i,paste0("ARIMA_S12_4_ASE")] = WindowedASE4
results[i,paste0("ARIMA_S12_5_ASE")] = WindowedASE5
results[i,paste0("ARIMA_S12_6_ASE")] = WindowedASE6
results[i,paste0("ARIMA_S12_7_ASE")] = WindowedASE7
results[i,paste0("ARIMA_S12_8_ASE")] = WindowedASE8
results[i,paste0("ARIMA_S12_9_ASE")] = WindowedASE9
results[i,paste0("ARIMA_S12_10_ASE")] = WindowedASE10
results[i,paste0("ARIMA_S12_11_ASE")] = WindowedASE11
results[i,paste0("ARIMA_S12_12_ASE")] = WindowedASE12
results[i,paste0("ARIMA_S12_F1")] = forecasts$f[1]
results[i,paste0("ARIMA_S12_F2")] = forecasts$f[2]
results[i,paste0("ARIMA_S12_F3")] = forecasts$f[3]
results[i,paste0("ARIMA_S12_F4")] = forecasts$f[4]
results[i,paste0("ARIMA_S12_F5")] = forecasts$f[5]
results[i,paste0("ARIMA_S12_F6")] = forecasts$f[6]
results[i,paste0("ARIMA_S12_F7")] = forecasts$f[7]
results[i,paste0("ARIMA_S12_F8")] = forecasts$f[8]
results[i,paste0("ARIMA_S12_F9")] = forecasts$f[9]
results[i,paste0("ARIMA_S12_F10")] = forecasts$f[10]
results[i,paste0("ARIMA_S12_F11")] = forecasts$f[11]
results[i,paste0("ARIMA_S12_F12")] = forecasts$f[12]
results[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
results[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
results[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
results[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
results[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
results[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
results[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
results[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
results[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
results[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
results[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
results[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]
#graph ASEs for each Model
EqualMeans_Results <- rbind(EqualMeans_Results_1,EqualMeans_Results_2,EqualMeans_Results_3,EqualMeans_Results_4,EqualMeans_Results_5,EqualMeans_Results_6,
EqualMeans_Results_7,EqualMeans_Results_8,EqualMeans_Results_9,EqualMeans_Results_10,EqualMeans_Results_11,EqualMeans_Results_12,
EqualMeans_Results_13)
ARMA_Results <- rbind(ARMA_Results_1,ARMA_Results_2,ARMA_Results_3,ARMA_Results_4,ARMA_Results_5,ARMA_Results_6,ARMA_Results_7,ARMA_Results_8,
ARMA_Results_9,ARMA_Results_10,ARMA_Results_11,ARMA_Results_12,ARMA_Results_13)
ARIMA_Results <- rbind(ARIMA_Results_1,ARIMA_Results_2,ARIMA_Results_3,ARIMA_Results_4,ARIMA_Results_5,ARIMA_Results_6,ARIMA_Results_7,ARIMA_Results_8,
ARIMA_Results_9,ARIMA_Results_10,ARIMA_Results_11,ARIMA_Results_12,ARIMA_Results_13)
ARIMAS_Results <- rbind(ARIMAS_Results_1,ARIMAS_Results_2,ARIMAS_Results_3,ARIMAS_Results_4,ARIMAS_Results_5,ARIMAS_Results_6,ARIMAS_Results_7,ARIMAS_Results_8,
ARIMAS_Results_9,ARIMAS_Results_10,ARIMAS_Results_11,ARIMAS_Results_12,ARIMAS_Results_13)
EqualMeans_Means <- colMeans(EqualMeans_Results)
ARMA_Means <- colMeans(ARMA_Results)
ARIMA_Means <- colMeans(ARIMA_Results)
ARIMAS_Means <- colMeans(ARIMAS_Results)
Combined_Means <- data.frame(EqualMeans_Means,ARMA_Means, ARIMA_Means, ARIMAS_Means)
Combined_Means$horizon <- as.numeric(row.names(Combined_Means))
g <- ggplot(data=Combined_Means, aes(horizon)) +
geom_line(aes(y=EqualMeans_Means, color="Equal Means"),size=1.5) +
geom_line(aes(y=ARMA_Means, color="ARMA"),size=1.5) +
geom_line(aes(y=ARIMA_Means, color="ARIMA"),size=1.5) +
geom_line(aes(y=ARIMAS_Means, color="ARIMAS"),size=1.5) +
scale_color_manual(values = c(
'Equal Means' = '#58508d',
'ARMA' = '#bc5090',
'ARIMA' = '#ff6361',
'ARIMAS' = '#ffa600'
)) +
labs(color='Models') +
scale_x_continuous(breaks=seq(0,13,1)) +
ggtitle(paste("Model ASEs for ", product,"and Customer",customer)) +
xlab("Month Ahead Forecast") +
ylab("ASE") +
theme(panel.background = element_blank(), axis.line = element_line(colour = "black"), legend.title = element_blank())
print(g)
}
The Ljung-Box test with K=10 has a p-value of 0.002322024 .The Ljung-Box test with K=24 has a p-value of 0.0034262 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.007674533 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."
The Ljung-Box test with K=10 has a p-value of 1.18705e-12 .The Ljung-Box test with K=24 has a p-value of 1.573741e-12 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.006130321 .The Ljung-Box test with K=24 has a p-value of 0.03101856 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.2367016 .The Ljung-Box test with K=24 has a p-value of 0.122692 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."
The Ljung-Box test with K=10 has a p-value of 9.303002e-10 .The Ljung-Box test with K=24 has a p-value of 1.985955e-07 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.004701657 .The Ljung-Box test with K=24 has a p-value of 0.232411 .[1] "Ljung-Box test results: At a significance level of 0.05, the test is inconclusive."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.02343884 .The Ljung-Box test with K=24 has a p-value of 0.1671774 .[1] "Ljung-Box test results: At a significance level of 0.05, the test is inconclusive."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.7619964 .The Ljung-Box test with K=24 has a p-value of 0.5395173 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 3.036074e-07 .The Ljung-Box test with K=24 has a p-value of 1.098736e-05 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.1572929 .The Ljung-Box test with K=24 has a p-value of 0.3914269 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.3857241 .The Ljung-Box test with K=24 has a p-value of 0.7674317 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 2.798171e-05 .The Ljung-Box test with K=24 has a p-value of 0.0008768368 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 3.111778e-09 .The Ljung-Box test with K=24 has a p-value of 1.111885e-09 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 6.819545e-12 .The Ljung-Box test with K=24 has a p-value of 7.58651e-10 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 9.048454e-08 .The Ljung-Box test with K=24 has a p-value of 5.283449e-07 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.0009021729 .The Ljung-Box test with K=24 has a p-value of 0.01759268 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is stationary."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 1.110223e-16 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0.0739774 .The Ljung-Box test with K=24 has a p-value of 0.1020833 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.1224362 .The Ljung-Box test with K=24 has a p-value of 0.4792812 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."
The Ljung-Box test with K=10 has a p-value of 0.1225766 .The Ljung-Box test with K=24 has a p-value of 0.5601297 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."
vec=c("EqualMeans_12_ASE","ARMA_12_ASE","ARIMA_12_ASE","ARIMA_S12_12_ASE")
results$winning_12 <- colnames(results[c("EqualMeans_12_ASE","ARMA_12_ASE","ARIMA_12_ASE","ARIMA_S12_12_ASE")])[apply(results[c("EqualMeans_12_ASE","ARMA_12_ASE","ARIMA_12_ASE","ARIMA_S12_12_ASE")],1,which.min)]
formattable(results, align = c("l", rep("r", NCOL(table_a) - 1)))| Product_Type | Product | Customer | ljung_10 | ljung_24 | ljung_results | top_5_bic | ADF | PP | KPSS | stationarity_results | EqualMeans_1_ASE | EqualMeans_2_ASE | EqualMeans_3_ASE | EqualMeans_4_ASE | EqualMeans_5_ASE | EqualMeans_6_ASE | EqualMeans_7_ASE | EqualMeans_8_ASE | EqualMeans_9_ASE | EqualMeans_10_ASE | EqualMeans_11_ASE | EqualMeans_12_ASE | EqualMeans_F1 | EqualMeans_F2 | EqualMeans_F3 | EqualMeans_F4 | EqualMeans_F5 | EqualMeans_F6 | EqualMeans_F7 | EqualMeans_F8 | EqualMeans_F9 | EqualMeans_F10 | EqualMeans_F11 | EqualMeans_F12 | ARMA_1_ASE | ARMA_2_ASE | ARMA_3_ASE | ARMA_4_ASE | ARMA_5_ASE | ARMA_6_ASE | ARMA_7_ASE | ARMA_8_ASE | ARMA_9_ASE | ARMA_10_ASE | ARMA_11_ASE | ARMA_12_ASE | ARMA_F1 | ARMA_F2 | ARMA_F3 | ARMA_F4 | ARMA_F5 | ARMA_F6 | ARMA_F7 | ARMA_F8 | ARMA_F9 | ARMA_F10 | ARMA_F11 | ARMA_F12 | ARIMA_1_ASE | ARIMA_2_ASE | ARIMA_3_ASE | ARIMA_4_ASE | ARIMA_5_ASE | ARIMA_6_ASE | ARIMA_7_ASE | ARIMA_8_ASE | ARIMA_9_ASE | ARIMA_10_ASE | ARIMA_11_ASE | ARIMA_12_ASE | ARIMA_F1 | ARIMA_F2 | ARIMA_F3 | ARIMA_F4 | ARIMA_F5 | ARIMA_F6 | ARIMA_F7 | ARIMA_F8 | ARIMA_F9 | ARIMA_F10 | ARIMA_F11 | ARIMA_F12 | ARIMA_S12_1_ASE | ARIMA_S12_2_ASE | ARIMA_S12_3_ASE | ARIMA_S12_4_ASE | ARIMA_S12_5_ASE | ARIMA_S12_6_ASE | ARIMA_S12_7_ASE | ARIMA_S12_8_ASE | ARIMA_S12_9_ASE | ARIMA_S12_10_ASE | ARIMA_S12_11_ASE | ARIMA_S12_12_ASE | ARIMA_S12_F1 | ARIMA_S12_F2 | ARIMA_S12_F3 | ARIMA_S12_F4 | ARIMA_S12_F5 | ARIMA_S12_F6 | ARIMA_S12_F7 | ARIMA_S12_F8 | ARIMA_S12_F9 | ARIMA_S12_F10 | ARIMA_S12_F11 | ARIMA_S12_F12 | ACTUAL_1 | ACTUAL_2 | ACTUAL_3 | ACTUAL_4 | ACTUAL_5 | ACTUAL_6 | ACTUAL_7 | ACTUAL_8 | ACTUAL_9 | ACTUAL_10 | ACTUAL_11 | ACTUAL_12 | winning_12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 700005925 | TAAKA VODKA 80 1L | 700005925 | 2.322024e-03 | 3.426200e-03 | not white noise | white noise | 0.16051598 | 0.01000000 | 0.08236679 | inconclusive | 819.7760806 | 812.0658241 | 815.1706105 | 689.8962088 | 601.4447370 | 535.9172216 | 489.1170549 | 453.3300453 | 418.8453911 | 390.5514370 | 364.9275910 | 346.4278690 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 51.2200000 | 1220.5831606 | 1064.5110370 | 1020.3968276 | 830.2558671 | 695.6295191 | 611.3732866 | 546.3263424 | 504.5024731 | 459.2102364 | 428.8023578 | 399.9887614 | 380.7868738 | 53.2174811 | 53.1162966 | 56.4704512 | 49.4069529 | 54.6932876 | 51.3134915 | 52.7815933 | 52.1860505 | 51.1159264 | 52.8831414 | 50.7506623 | 52.3671199 | 1.019355e+03 | 922.8713034 | 881.9550582 | 728.1959511 | 631.0542952 | 564.5865050 | 514.4789610 | 473.0086187 | 442.0050082 | 409.5462412 | 383.0871323 | 361.6927564 | 43.2661616 | 49.3228573 | 45.0704739 | 48.2247324 | 45.8328942 | 47.6618459 | 46.2589500 | 47.3362781 | 46.5086135 | 47.1445714 | 46.6558885 | 47.0314102 | 1057.5807655 | 1102.1703032 | 1124.8257798 | 1062.8228638 | 972.4991512 | 912.1410119 | 858.1841098 | 821.6447126 | 793.4708438 | 777.0434603 | 756.2249502 | 747.7752374 | 4.200000e+01 | 57.0000000 | 132.0000000 | 1.400000e+01 | 7.590000e+01 | 6.000000e+01 | 6.800000e+01 | 79.0000000 | 41.000000 | 70.00000000 | 54.000000 | 5.300000e+01 | 60 | 52.0 | 67 | 58 | 73 | 57 | 63.0 | 64.9 | 47.0 | 50 | 48 | 29.0 | EqualMeans_12_ASE |
| 701000317 | TAAKA VODKA 80 1L | 701000317 | 7.674533e-03 | 0.000000e+00 | not white noise | white noise | 0.01000000 | 0.01000000 | 0.10000000 | stationary | 5386.0238675 | 5396.0610470 | 6184.2691667 | 5551.7975855 | 5173.2864316 | 4930.6700214 | 4762.6696551 | 4625.7466239 | 4532.8720157 | 4471.5482265 | 4408.0742172 | 4359.0114744 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 101.7833333 | 5075.7624303 | 5322.5093370 | 5872.8687369 | 5059.3211299 | 4602.3842109 | 4469.0630501 | 4407.4131580 | 4192.1642408 | 4009.6761962 | 3890.3554742 | 3842.3155123 | 3826.2041051 | 95.1469980 | 111.2239452 | 130.6665597 | 134.9830893 | 132.6160184 | 120.0699014 | 107.4203227 | 94.9279002 | 87.1687948 | 84.0405840 | 86.5048168 | 92.1487011 | 1.067297e+04 | 8896.2364736 | 9681.2959002 | 7939.4196886 | 7844.4094248 | 7990.1810252 | 8554.5884303 | 8495.5687722 | 8648.9829702 | 8580.5019700 | 8400.6342571 | 8098.7569531 | 100.7928105 | 106.1108503 | 104.0874318 | 98.5400584 | 96.0526262 | 95.8392398 | 96.5603734 | 97.1166996 | 97.2837055 | 97.2210394 | 97.1236224 | 97.0748714 | 8433.3857923 | 5154.1237411 | 3763.1088122 | 2967.9427354 | 2477.4753201 | 2186.1939136 | 1971.8970771 | 1821.0071934 | 1703.7337292 | 1614.6880514 | 1527.2622155 | 1454.6370126 | 6.260246e+01 | 132.0000000 | 330.0000000 | 1.130000e+02 | 1.060000e+02 | 1.240000e+02 | 1.360000e+02 | 103.0000000 | 70.000000 | 25.00000000 | 47.000000 | 6.100000e+01 | 88 | 125.0 | 280 | 136 | 113 | 69 | 139.0 | 74.0 | 56.0 | 50 | 46 | 52.0 | ARIMA_S12_12_ASE |
| 701001770 | TAAKA VODKA 80 1L | 701001770 | 1.187050e-12 | 1.573741e-12 | not white noise | NA | 0.53188120 | 0.01000000 | 0.01000000 | not stationary | 6037.8142344 | 6011.6269267 | 6006.4802173 | 5164.7525036 | 4552.7806959 | 4119.4096190 | 3804.3090329 | 3566.8000677 | 3361.0108897 | 3202.4520857 | 3057.9253719 | 2878.2446917 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 106.4600000 | 6069.9661721 | 5828.9569556 | 5547.8444068 | 4610.1606213 | 3791.3806203 | 3434.4124271 | 3067.2728007 | 2758.3131160 | 2544.1935701 | 2414.8295759 | 2316.1141232 | 2178.9429165 | 126.1569793 | 146.0084226 | 143.7054915 | 138.8871720 | 139.8964381 | 139.0296243 | 137.7483457 | 137.0800734 | 136.2793895 | 135.4398483 | 134.6801564 | 133.9294398 | 5.254440e+03 | 4999.1257339 | 5154.8823639 | 4783.7655494 | 4074.9633382 | 3593.7634359 | 3216.2823825 | 2939.4821732 | 2754.5828734 | 2607.4836920 | 2519.5146881 | 2417.0835426 | 130.6083974 | 149.5099179 | 167.8357808 | 158.6284493 | 146.5277043 | 151.2585751 | 159.1897122 | 156.5399797 | 151.7689753 | 152.9420884 | 155.9654258 | 155.4518223 | 6366.8174714 | 6162.0168690 | 6965.4999529 | 6622.7382835 | 6228.5606941 | 6005.9191192 | 5770.7234801 | 5585.5098089 | 5469.6374123 | 5399.0224535 | 5393.4726932 | 5417.6119722 | 1.290000e+02 | 138.0000000 | 307.0000000 | 7.000000e+00 | 1.550000e+02 | 1.270000e+02 | 1.180000e+02 | 154.0000000 | 92.000000 | 148.00000000 | 192.000000 | 1.620000e+02 | 147 | 117.0 | 142 | 133 | 111 | 83 | 95.0 | 114.0 | 91.9 | 104 | 117 | 100.0 | ARMA_12_ASE |
| 701001790 | TAAKA VODKA 80 1L | 701001790 | 6.130321e-03 | 3.101856e-02 | not white noise | NA | 0.23862134 | 0.01000000 | 0.10000000 | inconclusive | 656.5598284 | 653.9191489 | 657.4544780 | 565.9303476 | 481.6666900 | 426.3206618 | 387.9143779 | 358.5476137 | 336.9679082 | 318.7005028 | 304.7056093 | 294.3995806 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 47.6116667 | 786.6821475 | 714.5797864 | 711.4097381 | 607.2602509 | 513.3486510 | 460.5636041 | 418.4143139 | 384.0363764 | 356.1047069 | 333.7082767 | 316.0337581 | 303.6017446 | 50.1138106 | 56.0235607 | 52.5582075 | 52.5577752 | 51.5403314 | 51.0307437 | 50.4769171 | 50.0500161 | 49.6736841 | 49.3599313 | 49.0923578 | 48.8662770 | 8.578247e+02 | 740.6271509 | 750.6761298 | 646.1743870 | 547.8952825 | 502.9643017 | 458.7333820 | 422.7623404 | 390.8696895 | 368.0898651 | 352.1400245 | 344.3114579 | 52.6895755 | 58.3425279 | 56.6876771 | 57.1721197 | 57.0303035 | 57.0718189 | 57.0596657 | 57.0632234 | 57.0621819 | 57.0624868 | 57.0623976 | 57.0624237 | 842.6917713 | 898.1286013 | 959.1236222 | 904.9257325 | 814.4104498 | 774.4453964 | 743.4284306 | 731.9260579 | 714.1077562 | 702.2044549 | 696.7813044 | 699.6595046 | 6.789311e+01 | 55.1070490 | 119.9267300 | 6.368655e+00 | 5.489771e+01 | 5.193155e+01 | 5.440356e+01 | 55.3706734 | 35.177312 | 54.14892463 | 59.076715 | 7.206030e+01 | 63 | 64.9 | 59 | 55 | 52 | 39 | 35.0 | 44.0 | 32.0 | 40 | 33 | 28.9 | EqualMeans_12_ASE |
| 700005448 | TAAKA VODKA 80 1L | 700005448 | 2.367016e-01 | 1.226920e-01 | white noise | white noise | 0.01000000 | 0.01000000 | 0.10000000 | stationary | 3.2606182 | 3.2721566 | 3.2434387 | 3.0333105 | 2.7925156 | 2.5995498 | 2.4645339 | 2.3359643 | 2.2364786 | 2.1533002 | 2.0775063 | 2.0241096 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 3.3155536 | 3.6951052 | 3.5728124 | 3.2893304 | 2.9938501 | 2.7727916 | 2.6125905 | 2.4612121 | 2.3474646 | 2.2538158 | 2.1690031 | 2.1081807 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 2.7483333 | 4.277557e+00 | 4.4170716 | 4.2540623 | 4.2082053 | 4.0010940 | 3.7620384 | 3.5477853 | 3.2918129 | 3.0336648 | 2.8995667 | 2.7235312 | 2.6498099 | 2.0911105 | 2.3396315 | 1.6856053 | 1.7126542 | 1.6028931 | 1.6049587 | 1.5864818 | 1.5864097 | 1.5832898 | 1.5832066 | 1.5826781 | 1.5826521 | 5.2717011 | 4.8712880 | 4.5640162 | 4.1850058 | 3.8107385 | 3.6754518 | 3.5445104 | 3.4088147 | 3.2588620 | 3.1409703 | 3.0572035 | 3.1602990 | 4.394872e+00 | 3.5629699 | 5.9933855 | -6.026074e-01 | 8.879026e-01 | 3.114198e+00 | 9.120087e-01 | 3.1909435 | 2.023524 | 3.96196530 | 4.055599 | 5.935030e+00 | 3 | 4.0 | 3 | 2 | 3 | 2 | 1.9 | 2.0 | 2.0 | 3 | 2 | 1.0 | EqualMeans_12_ASE |
| 700005910 | TAAKA VODKA 80 1L | 700005910 | 9.303002e-10 | 1.985955e-07 | not white noise | NA | 0.41243058 | 0.01000000 | 0.01000000 | not stationary | 6.7172506 | 6.7250712 | 6.5282763 | 5.5460968 | 4.8189942 | 4.3354985 | 3.8306572 | 3.4450071 | 3.1375640 | 2.8975071 | 2.7124721 | 2.5533618 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 3.5983333 | 6.1013892 | 5.9203572 | 5.1397653 | 5.1470264 | 4.7179650 | 4.3067151 | 3.9056435 | 3.4903498 | 3.2598653 | 3.0606990 | 2.8924495 | 2.7913065 | 3.9108782 | 3.8589130 | 4.3650583 | 3.8193368 | 3.7658267 | 4.0203365 | 3.7464232 | 3.7050224 | 3.8320614 | 3.6942498 | 3.6657190 | 3.7285952 | 6.418067e+00 | 5.5822237 | 5.1910526 | 5.7611289 | 5.3900833 | 4.9376795 | 4.7755047 | 4.4630113 | 4.2442940 | 4.1784287 | 4.1535670 | 4.0361142 | 4.1969130 | 4.1858766 | 4.7215529 | 4.2985980 | 4.2868719 | 4.5737411 | 4.3510523 | 4.3417089 | 4.4952930 | 4.3780807 | 4.3714635 | 4.4536672 | 12.9033412 | 14.3702306 | 13.6094087 | 12.4329890 | 13.0086409 | 12.1494337 | 11.3515892 | 10.8322386 | 10.5849708 | 10.3442391 | 10.3014626 | 10.5715793 | 2.827593e+00 | 5.0647919 | 9.9032571 | -2.211545e-01 | 3.837791e+00 | 7.005361e+00 | 1.897978e+00 | 5.0104979 | 2.971441 | 3.98968502 | 4.001390 | 4.989016e+00 | 3 | 4.0 | 3 | 3 | 3 | 3 | 3.0 | 3.0 | 2.0 | 3 | 2 | 4.0 | EqualMeans_12_ASE |
| 701001906 | TAAKA VODKA 80 1L | 701001906 | 4.701657e-03 | 2.324110e-01 | inconclusive | white noise | 0.25007229 | 0.01000000 | 0.05352414 | inconclusive | 65.2421581 | 65.6767735 | 65.4695085 | 59.6613889 | 55.7436966 | 53.1857479 | 51.1165171 | 49.5479274 | 47.2526994 | 45.3416453 | 42.9647688 | 40.5688675 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 8.1166667 | 85.6532674 | 78.3684495 | 78.3403061 | 75.3847626 | 70.1241569 | 67.8788493 | 64.9288995 | 62.8958034 | 60.2088286 | 57.8759763 | 55.0380537 | 51.8806305 | 14.4341932 | 14.2992145 | 14.2981344 | 13.8378853 | 13.5695530 | 13.3717741 | 13.1063023 | 12.8707520 | 12.6607333 | 12.4485251 | 12.2471629 | 12.0581166 | 7.502760e+01 | 72.4998836 | 66.2607202 | 62.0471258 | 56.6378845 | 53.7960147 | 51.3101253 | 50.7398992 | 50.4118597 | 51.3105130 | 50.7607084 | 49.5530079 | 16.8900802 | 14.4266741 | 16.4785885 | 15.8949595 | 15.5535072 | 16.2036223 | 15.5111407 | 15.9504079 | 15.9285781 | 15.6921148 | 15.9496297 | 15.7800948 | 70.6317652 | 70.6193852 | 84.1328390 | 86.1232897 | 87.6434001 | 87.6274218 | 86.3545689 | 89.4743434 | 92.0583899 | 95.7837302 | 98.3255336 | 99.7407462 | 1.378831e+01 | 16.7230399 | 31.2335027 | 6.236520e+00 | 1.494705e+01 | 1.903011e+01 | 1.666967e+01 | 23.7685567 | 15.962763 | 22.18950698 | 19.465098 | 2.001956e+01 | 5 | 10.0 | 8 | 12 | 11 | 7 | 5.0 | 4.0 | 4.0 | 7 | 5 | 10.0 | EqualMeans_12_ASE |
| 701001907 | TAAKA VODKA 80 1L | 701001907 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.42321723 | 0.01000000 | 0.01000000 | not stationary | 198.1483532 | 202.6365583 | 206.4005754 | 182.9596994 | 171.3135840 | 163.8738660 | 158.2928221 | 155.6318788 | 153.1012307 | 151.9063532 | 150.0285164 | 147.7516011 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 15.5316667 | 163.0706045 | 147.6514991 | 142.0327887 | 118.6811530 | 102.0842851 | 93.9061365 | 88.8143283 | 89.1300378 | 90.6734892 | 93.6587780 | 96.6549372 | 98.3048675 | 22.8958642 | 23.2461938 | 22.9222282 | 22.5535981 | 22.4030964 | 22.1708292 | 21.9334597 | 21.7335775 | 21.5290731 | 21.3288296 | 21.1394194 | 20.9548197 | 1.501983e+02 | 143.3290122 | 141.7302822 | 119.6492689 | 106.8935998 | 97.5921329 | 92.7298300 | 94.7295674 | 97.4315877 | 102.3187664 | 106.9094471 | 111.2762217 | 22.9247349 | 23.6428572 | 23.5853520 | 23.4369136 | 23.5165456 | 23.5172404 | 23.4976499 | 23.5061535 | 23.5071332 | 23.5046404 | 23.5055066 | 23.5057268 | 182.8480991 | 165.3978276 | 172.7950756 | 165.8161092 | 160.9457245 | 156.9136823 | 154.9305126 | 158.5704392 | 161.8352075 | 168.1169377 | 174.1008125 | 178.8359459 | 1.700000e+01 | 21.0000000 | 50.0000000 | 1.000000e+00 | 2.200000e+01 | 2.500000e+01 | 1.900000e+01 | 27.0000000 | 19.000000 | 27.00000000 | 25.000000 | 2.400000e+01 | 28 | 25.0 | 26 | 23 | 30 | 22 | 7.0 | 4.0 | 5.0 | 5 | 8 | 21.0 | ARMA_12_ASE |
| 700005900 | TAAKA VODKA 80 1L | 700005900 | 2.343884e-02 | 1.671774e-01 | inconclusive | white noise | 0.18041707 | 0.01000000 | 0.04977124 | not stationary | 1.1002137 | 1.2694444 | 1.3378205 | 1.4354701 | 1.5084188 | 1.5634615 | 1.6097375 | 1.6434829 | 1.6663105 | 1.6832906 | 1.7279526 | 1.7576923 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.0595516 | 1.3538109 | 1.4839001 | 1.5426432 | 1.5814597 | 1.6259222 | 1.6660457 | 1.6941691 | 1.7063527 | 1.7177220 | 1.7584874 | 1.7871770 | 2.5412846 | 2.2836974 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.8833333 | 1.101310e+00 | 1.3801037 | 1.3854369 | 1.5228097 | 1.5577902 | 1.5402714 | 1.5416878 | 1.5752095 | 1.5914634 | 1.6536299 | 1.7103440 | 1.7389881 | 1.2338905 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.0000244 | 1.1350347 | 1.5327785 | 1.7377441 | 2.0966865 | 2.4001221 | 2.5704244 | 2.7177394 | 2.8033499 | 2.8996504 | 2.9787477 | 3.0430483 | 3.0968104 | 3.179249e+00 | 1.6499882 | 3.0000000 | 0.000000e+00 | 1.000000e+00 | 2.000000e+00 | 3.000000e+00 | 3.0000000 | 3.000000 | 2.00000000 | 3.000000 | 3.000000e+00 | 3 | 4.0 | 3 | 4 | 4 | 3 | 1.0 | 3.0 | 1.0 | 3 | 4 | 2.0 | ARIMA_12_ASE |
| 701001768 | TAAKA VODKA 80 1L | 701001768 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.48537100 | 0.01000000 | 0.10000000 | inconclusive | 4.8252590 | 4.7309000 | 4.6891906 | 4.6548744 | 4.4625923 | 4.1009000 | 3.8908267 | 3.6955154 | 3.6434926 | 3.5806949 | 3.4830212 | 3.3908573 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 4.7800000 | 5.2605927 | 5.2971241 | 5.2878247 | 5.1661669 | 4.8449283 | 4.4788421 | 4.1976426 | 3.9212539 | 3.8133806 | 3.6862767 | 3.5379249 | 3.3946633 | 5.2292753 | 5.1602537 | 5.1018358 | 5.0523925 | 5.0105452 | 4.9751268 | 4.9451497 | 4.9197779 | 4.8983040 | 4.8801291 | 4.8647464 | 4.8517269 | 5.732139e+00 | 5.7316454 | 5.9547820 | 5.9448081 | 5.6364189 | 5.3917974 | 5.0619394 | 4.6936530 | 4.5424800 | 4.3541588 | 4.1646626 | 3.9649667 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 5.0704608 | 4.9079529 | 4.9796347 | 5.0235500 | 5.3625069 | 5.1204962 | 4.9727518 | 4.8140382 | 4.7272246 | 4.7013188 | 4.6820765 | 4.7368283 | 4.7764556 | 4.750496e+00 | 5.5412219 | 6.3569667 | 9.194740e+00 | 1.051907e+00 | 3.926150e+00 | 2.815428e+00 | 3.7179421 | 3.632111 | 2.55654143 | 6.490006 | 6.431425e+00 | 4 | 5.0 | 4 | 5 | 4 | 3 | 2.0 | 3.0 | 1.0 | 5 | 4 | 4.0 | EqualMeans_12_ASE |
| 700005850 | TAAKA VODKA 80 1L | 700005850 | 7.619964e-01 | 5.395173e-01 | white noise | white noise | 0.05366716 | 0.01000000 | 0.10000000 | inconclusive | 0.7946959 | 0.8499524 | 0.8584566 | 0.8650806 | 0.8504908 | 0.8458498 | 0.8291648 | 0.8163306 | 0.8088270 | 0.8013113 | 0.7960479 | 0.7916831 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 0.9313236 | 0.9150902 | 0.8734208 | 0.8846560 | 0.8540705 | 0.8458284 | 0.8180487 | 0.7992410 | 0.8014471 | 0.7953921 | 0.7858098 | 0.7843329 | 1.1990399 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.6633333 | 1.668124e+00 | 1.7099588 | 1.4339802 | 1.4716291 | 1.4078535 | 1.4279774 | 1.3607470 | 1.3316285 | 1.2889480 | 1.2815764 | 1.2452635 | 1.2593410 | -0.2756279 | 0.6273774 | 0.3784424 | 0.4470673 | 0.4281492 | 0.4333644 | 0.4319267 | 0.4323230 | 0.4322138 | 0.4322439 | 0.4322356 | 0.4322379 | 2.2656312 | 2.5005957 | 2.5645920 | 2.5893030 | 2.5160865 | 2.4683782 | 2.4140848 | 2.3876108 | 2.3643841 | 2.3484751 | 2.3305555 | 2.3184846 | 1.250166e+00 | 1.0000000 | 3.0000000 | 0.000000e+00 | 2.000000e+00 | 3.000000e+00 | 2.000000e+00 | 2.0000000 | 1.000000 | 2.00000000 | 2.000000 | 3.000000e+00 | 1 | 3.0 | 2 | 3 | 3 | 1 | 1.0 | 2.0 | 1.0 | 1 | 1 | 2.0 | ARMA_12_ASE |
| 701001830 | TAAKA VODKA 80 1L | 701001830 | 3.036074e-07 | 1.098736e-05 | not white noise | NA | 0.01094855 | 0.01000000 | 0.01000000 | inconclusive | 3.3812607 | 3.3274145 | 3.5419444 | 3.2107479 | 2.9817735 | 2.8650214 | 2.8658761 | 2.8812607 | 2.8883832 | 2.8969017 | 2.9194891 | 2.9395940 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 4.0075461 | 3.4573960 | 3.5632091 | 3.2119952 | 2.9633191 | 2.8283792 | 2.8212973 | 2.8343839 | 2.8403766 | 2.8490921 | 2.8750325 | 2.8932145 | 2.6117949 | 2.5657214 | 2.5242446 | 2.4869061 | 2.4532928 | 2.4230331 | 2.3957925 | 2.3712696 | 2.3491934 | 2.3293198 | 2.3114290 | 2.2953231 | 5.693141e+00 | 5.0198774 | 5.5617559 | 5.3414683 | 5.1786422 | 5.1347258 | 5.2635862 | 5.2865471 | 5.2943238 | 5.2846495 | 5.1757291 | 5.0886369 | 1.3356365 | 1.5349088 | 1.2718390 | 1.1519197 | 1.0750150 | 1.0476987 | 1.0247556 | 1.0139917 | 1.0077459 | 1.0043690 | 1.0024185 | 1.0013730 | 4.7621704 | 4.6118544 | 4.6386722 | 4.2674657 | 4.0447418 | 3.8577976 | 3.8231672 | 3.7875790 | 3.7342582 | 3.6916017 | 3.6776798 | 3.6660783 | 4.000000e+00 | 2.0000000 | 7.0000000 | 0.000000e+00 | 3.000000e+00 | 3.000000e+00 | 2.000000e+00 | 3.0000000 | 3.000000 | 2.00000000 | 3.000000 | 4.000000e+00 | 3 | 4.0 | 5 | 4 | 3 | 4 | 5.0 | 3.0 | 2.0 | 3 | 1 | 3.0 | ARMA_12_ASE |
| 701001767 | TAAKA VODKA 80 1L | 701001767 | 1.572929e-01 | 3.914269e-01 | white noise | white noise | 0.34274666 | 0.01000000 | 0.10000000 | inconclusive | 1.3459188 | 1.3023291 | 1.2066026 | 1.0946368 | 1.0100214 | 0.9544658 | 0.9140507 | 0.8667521 | 0.8387963 | 0.8400214 | 0.8181799 | 0.7995513 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 2.2166667 | 1.9333380 | 1.6235733 | 1.4734965 | 1.3692537 | 1.2889112 | 1.1850200 | 1.1032948 | 1.0376552 | 0.9962394 | 0.9859819 | 0.9518440 | 0.9239290 | 2.3807007 | 2.1586414 | 2.9171391 | 2.5688481 | 2.2957120 | 2.3980851 | 2.2483458 | 2.5293585 | 2.3935057 | 2.3247667 | 2.3487997 | 2.2723652 | 1.750115e+00 | 1.6015794 | 1.4961143 | 1.4375831 | 1.3589958 | 1.2541742 | 1.1713232 | 1.1220013 | 1.0900889 | 1.0678670 | 1.0191809 | 0.9856034 | 2.4672700 | 2.3263118 | 3.1237031 | 2.7179263 | 2.4276452 | 2.5866173 | 2.4886757 | 2.8069577 | 2.6373311 | 2.5623943 | 2.6135525 | 2.5630514 | 3.5248317 | 3.1975521 | 3.0058058 | 2.8039407 | 2.5891514 | 2.4424681 | 2.3937548 | 2.2516280 | 2.1680245 | 2.1171107 | 2.0662856 | 2.0406461 | 1.388334e+00 | -0.1222036 | 4.3714579 | 9.221621e-01 | 1.751937e+00 | 2.126097e+00 | 9.330889e-01 | 2.1345194 | 1.948275 | 3.94710235 | 3.034467 | 1.974070e+00 | 1 | 2.0 | 1 | 2 | 2 | 2 | 2.0 | 2.0 | 1.0 | 4 | 2 | 3.0 | EqualMeans_12_ASE |
| 701001810 | TAAKA VODKA 80 1L | 701001810 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.54437889 | 0.01000000 | 0.01060199 | not stationary | 2.7694231 | 2.9386538 | 3.0241239 | 2.5476282 | 2.2068590 | 1.9775427 | 1.8086172 | 1.6787179 | 1.5862322 | 1.5060897 | 1.4374883 | 1.3850214 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 2.1500000 | 4.5910109 | 4.3387866 | 4.0374311 | 3.4712152 | 3.0265545 | 2.7291639 | 2.5120868 | 2.3031515 | 2.1768817 | 2.0924796 | 1.9910859 | 1.8807362 | 1.9994117 | 2.0113054 | 2.0222596 | 2.0323487 | 2.0416410 | 2.0501993 | 2.0580817 | 2.0653416 | 2.0720280 | 2.0781863 | 2.0838583 | 2.0890822 | 4.163263e+00 | 4.1005963 | 3.8469651 | 3.5846134 | 3.2781221 | 3.0622591 | 2.8507899 | 2.7383287 | 2.5955131 | 2.6034540 | 2.5522387 | 2.4843749 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 1.9763079 | 4.2968421 | 4.2911908 | 4.8025444 | 5.3729971 | 5.2736339 | 5.1200821 | 5.0757839 | 4.9578981 | 4.8594204 | 4.7532709 | 4.6769437 | 4.5169437 | 1.511649e+00 | 1.5856716 | 6.6484741 | -2.982427e-01 | 1.746964e+00 | 1.785318e+00 | 1.817859e+00 | 1.8454674 | 0.868891 | 1.88876405 | 1.905625 | 1.919930e+00 | 0 | 0.0 | 1 | 2 | 2 | 2 | 2.0 | 2.0 | 1.0 | 2 | 2 | 1.0 | EqualMeans_12_ASE |
| 700005866 | TAAKA VODKA 80 1L | 700005866 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.31221025 | 0.02148804 | 0.03174915 | not stationary | 41.0203241 | 39.3216062 | 37.4481019 | 36.1557088 | 34.5091447 | 32.8639994 | 31.5960751 | 30.2733370 | 28.8379310 | 27.3446318 | 25.8320957 | 24.2926318 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 7.3283333 | 2.0775360 | 2.3394179 | 2.5571922 | 2.9196070 | 3.1780195 | 3.4797540 | 4.2895843 | 5.0141588 | 5.4157855 | 5.5611932 | 5.6039443 | 5.5032397 | 3.1421683 | 4.7655097 | 4.2451054 | 4.9756542 | 4.9146008 | 5.2965478 | 5.3803732 | 5.6156141 | 5.7338443 | 5.8991854 | 6.0148171 | 6.1410207 | 2.214432e+00 | 2.4734601 | 2.8964279 | 3.4077682 | 4.0111561 | 4.7870135 | 6.4359796 | 8.1630524 | 9.6417922 | 11.0790659 | 12.4832663 | 13.8160406 | 2.5152302 | 4.0587504 | 3.0999274 | 3.6955410 | 3.3255503 | 3.5553857 | 3.4126137 | 3.5013026 | 3.4462097 | 3.4804330 | 3.4591738 | 3.4723798 | 9.2666327 | 8.9026054 | 10.6855680 | 13.0907783 | 15.4853964 | 17.6714293 | 20.6486179 | 23.4194441 | 25.6164912 | 27.6086889 | 29.5849732 | 31.2513160 | 6.541185e-01 | 2.0293576 | 3.2816330 | 8.918506e-01 | 1.890484e+00 | 2.598173e+00 | 1.513890e+00 | 0.4059347 | 1.314475 | 1.25664156 | 1.200629 | 5.160187e+00 | 4 | 4.0 | 5 | 4 | 7 | 7 | 12.0 | 5.0 | 4.0 | 7 | 6 | 7.0 | ARMA_12_ASE |
| 701001880 | TAAKA VODKA 80 1L | 701001880 | 3.857241e-01 | 7.674317e-01 | white noise | white noise | 0.02966138 | 0.01000000 | 0.01000000 | inconclusive | 1.4269017 | 1.4461325 | 1.4610897 | 1.4794658 | 1.4438248 | 1.4059615 | 1.3686600 | 1.3381197 | 1.3157906 | 1.2974145 | 1.2604681 | 1.1828846 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.5174396 | 1.4948883 | 1.4825224 | 1.5006991 | 1.4644323 | 1.4215440 | 1.3823838 | 1.3492160 | 1.3240311 | 1.3028449 | 1.2655291 | 1.1871722 | 1.1998213 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 1.3666667 | 2.006564e+00 | 2.3342891 | 2.3004118 | 2.3140128 | 2.2600330 | 2.2419669 | 2.2286639 | 2.2570145 | 2.3453982 | 2.3518083 | 2.3005831 | 2.2235996 | 2.2651424 | 2.8990216 | 2.4129341 | 2.0937681 | 2.4508967 | 2.4996365 | 2.3321244 | 2.3382486 | 2.4198043 | 2.3981070 | 2.3645226 | 2.3816840 | 3.1199556 | 3.1503628 | 2.7148049 | 2.6544759 | 2.6625206 | 2.6213930 | 2.4272105 | 2.3303058 | 2.2490123 | 2.1530840 | 2.0921738 | 2.0336181 | 6.240092e-01 | 1.3893508 | 0.4234414 | 1.629559e+00 | -6.083827e-01 | -5.406915e-01 | 9.984264e-01 | 0.1504591 | 1.624386 | 2.57950379 | 3.559803 | 8.524046e-01 | 2 | 2.0 | 2 | 2 | 1 | 1 | 2.0 | 1.0 | 1.0 | 2 | 1 | 2.0 | EqualMeans_12_ASE |
| 700005861 | TAAKA VODKA 80 1L | 700005861 | 2.798171e-05 | 8.768368e-04 | not white noise | NA | 0.11665129 | 0.01000000 | 0.04796742 | not stationary | 3.1449053 | 3.4033669 | 3.4895207 | 3.0920848 | 2.8322387 | 2.6534524 | 2.5257478 | 2.4283669 | 2.3526261 | 2.2995464 | 2.2598471 | 2.2449908 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 1.2783333 | 2.9120469 | 3.2251489 | 3.3751316 | 3.1821920 | 2.9660736 | 2.8280312 | 2.6700627 | 2.5279470 | 2.3702667 | 2.2522066 | 2.1634190 | 2.1149156 | 1.9633104 | 1.8684188 | 1.7866728 | 1.7162512 | 1.6555854 | 1.6033237 | 1.5583020 | 1.5195172 | 1.4861054 | 1.4573222 | 1.4325264 | 1.4111657 | 2.962186e+00 | 3.4010894 | 3.5663049 | 3.4222635 | 3.2474177 | 3.0839616 | 2.9365710 | 2.7409038 | 2.5170765 | 2.3283588 | 2.1689325 | 2.0708163 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 2.0995448 | 6.0699551 | 5.8170034 | 5.8041211 | 5.1472329 | 4.7108524 | 4.4383617 | 4.1424992 | 3.8847447 | 3.6384809 | 3.4857644 | 3.3418270 | 3.2749200 | 2.156258e+00 | 3.1286190 | 6.1058690 | 8.714302e-02 | 2.071729e+00 | 1.059042e+00 | 1.048599e+00 | 1.0400025 | 1.032927 | 1.02710284 | 2.022309 | 4.018363e+00 | 3 | 4.0 | 3 | 2 | 1 | 2 | 1.0 | 1.0 | 1.0 | 2 | 1 | 3.0 | ARIMA_12_ASE |
| 701001850 | TAAKA VODKA 80 1L | 701001850 | 3.111778e-09 | 1.111885e-09 | not white noise | NA | 0.01000000 | 0.01000000 | 0.01000000 | inconclusive | 1.6864744 | 1.6531410 | 1.6420299 | 1.6210897 | 1.6695513 | 1.6646795 | 1.6198077 | 1.6082692 | 1.5995798 | 1.5944231 | 1.5687587 | 1.5544231 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 1.7833333 | 0.9471051 | 0.9410728 | 0.9583839 | 0.9320713 | 1.0150731 | 1.0192416 | 0.9862771 | 0.9582185 | 0.9320831 | 0.9355995 | 0.9036402 | 0.8910035 | 0.6945360 | 1.3803241 | 0.8504484 | 1.1642663 | 1.0882857 | 1.0855645 | 1.1544780 | 1.1234983 | 1.1647393 | 1.1702968 | 1.1837013 | 1.2018058 | 1.231704e+00 | 1.3687870 | 1.4382336 | 1.2802140 | 1.2448374 | 1.1547863 | 1.0938548 | 1.0693608 | 1.0896346 | 1.0644152 | 1.0024592 | 0.9485882 | 0.7516630 | 1.2945436 | 0.6991328 | 1.2715343 | 1.0815054 | 0.8580775 | 1.1862125 | 0.9383167 | 1.0657447 | 1.0882255 | 0.9535772 | 1.0939614 | 1.8266180 | 1.9893472 | 1.8271548 | 2.1182253 | 1.9236300 | 1.8966680 | 1.7713696 | 1.7231753 | 1.6788265 | 1.6423503 | 1.6187286 | 1.5899860 | 1.649683e+00 | 0.4027416 | 0.2461327 | 2.052215e+00 | -1.627674e-01 | 1.252866e-01 | 9.607176e-01 | 0.9776946 | 1.038822 | -0.02528883 | 2.005146 | 1.007060e+00 | 2 | 2.0 | 1 | 0 | 0 | 1 | 2.0 | 0.0 | 1.0 | 1 | 1 | 1.0 | ARMA_12_ASE |
| 701001901 | TAAKA VODKA 80 1L | 701001901 | 6.819545e-12 | 7.586510e-10 | not white noise | NA | 0.18541887 | 0.01000000 | 0.01000000 | not stationary | 0.7879701 | 1.0213034 | 1.1033547 | 1.1533547 | 1.1454060 | 1.1285684 | 1.1388858 | 1.1482265 | 1.1731553 | 1.1741239 | 1.1772475 | 1.1804915 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 0.7687278 | 0.8821437 | 0.9522771 | 0.9727396 | 0.9590509 | 0.9318883 | 0.9316880 | 0.9346157 | 0.9576802 | 0.9540655 | 0.9598836 | 0.9652515 | 1.8236440 | 1.7776671 | 1.7389717 | 1.7064044 | 1.6789949 | 1.6559263 | 1.6365111 | 1.6201707 | 1.6064181 | 1.5948436 | 1.5851021 | 1.5769034 | 7.399023e-01 | 0.8315413 | 0.8883643 | 0.8961124 | 0.8765321 | 0.8336705 | 0.8133006 | 0.7998427 | 0.8038369 | 0.7852240 | 0.7804549 | 0.7791951 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 1.9453676 | 0.6230959 | 0.8141515 | 0.8558566 | 0.9235350 | 0.9969168 | 1.0146397 | 1.0315406 | 1.0370816 | 1.0421818 | 1.0407774 | 1.0285619 | 1.0280019 | 6.237002e-01 | 1.8583984 | 0.9467154 | 2.979949e+00 | -7.545188e-03 | 1.997161e+00 | 1.998932e+00 | 1.9995980 | 2.999849 | 1.99994307 | 1.999979 | 1.999992e+00 | 1 | 4.0 | 2 | 2 | 2 | 2 | 3.0 | 2.0 | 3.0 | 2 | 2 | 1.0 | ARIMA_12_ASE |
| 701001904 | TAAKA VODKA 80 1L | 701001904 | 9.048454e-08 | 5.283449e-07 | not white noise | NA | 0.43473483 | 0.01000000 | 0.01000000 | not stationary | 1.1955769 | 1.2096795 | 1.2229274 | 1.2218590 | 1.2048077 | 1.1964316 | 1.1941117 | 1.1949359 | 1.1944373 | 1.1976282 | 1.2035023 | 1.2069017 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4666667 | 1.4841602 | 1.5389074 | 1.4902713 | 1.4144033 | 1.3738584 | 1.3599818 | 1.3405575 | 1.3257438 | 1.3175436 | 1.3013227 | 1.3052061 | 1.3102041 | 1.5810320 | 2.0646698 | 2.6573867 | 1.9097428 | 1.9640995 | 1.9062874 | 1.9416191 | 1.7303295 | 1.7743717 | 1.7186676 | 1.6788633 | 1.6447738 | 1.282673e+00 | 1.5206545 | 1.4229317 | 1.3809908 | 1.4082162 | 1.4251940 | 1.4167668 | 1.4330891 | 1.4325368 | 1.4267040 | 1.4439083 | 1.4253409 | 1.8423873 | 2.4863038 | 3.2129767 | 2.5352098 | 2.6448515 | 2.6991264 | 2.8165294 | 2.6127613 | 2.7216841 | 2.7222384 | 2.6995275 | 2.6989619 | 3.0800760 | 2.3915354 | 2.3939485 | 2.4090143 | 2.4395653 | 2.3694690 | 2.3644406 | 2.3630603 | 2.3654867 | 2.3960114 | 2.4235625 | 2.3890228 | 1.143407e+00 | 2.2319445 | 4.0112431 | 1.447822e-01 | 1.509765e+00 | 1.494126e+00 | 1.106289e+00 | 2.2140312 | 1.235630 | 1.06777297 | 3.091769 | 4.110406e+00 | 2 | 2.0 | 2 | 3 | 1 | 2 | 2.0 | 1.0 | 2.0 | 2 | 2 | 3.0 | EqualMeans_12_ASE |
| 701000321 | TAAKA VODKA 80 1L | 701000321 | 9.021729e-04 | 1.759268e-02 | not white noise | NA | 0.01899300 | 0.01000000 | 0.10000000 | stationary | 1.1710043 | 1.2004915 | 1.2094658 | 1.0908761 | 0.9925427 | 0.9056197 | 0.8398687 | 0.7668376 | 0.7063319 | 0.6671581 | 0.6332420 | 0.6049786 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 1.2166667 | 4.9505043 | 2.9344969 | 2.3457840 | 2.5624829 | 2.4150441 | 2.2656664 | 2.1414018 | 1.9553184 | 1.8213283 | 1.7053062 | 1.6001769 | 1.4984614 | 1.5723548 | 1.4633890 | 1.5054031 | 1.2272708 | 1.0921195 | 1.0500487 | 1.0002845 | 1.0361209 | 1.1136744 | 1.1867192 | 1.2578197 | 1.3051289 | 1.322547e+00 | 1.7211078 | 1.8703293 | 1.9101641 | 1.8088129 | 1.6926424 | 1.6207221 | 1.5910010 | 1.5188421 | 1.4191297 | 1.3462616 | 1.3141439 | 1.2204117 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 1.0000166 | 0.8263359 | 0.7231268 | 0.9128621 | 1.1243435 | 1.1876421 | 1.1582706 | 1.1786536 | 1.1696388 | 1.1729235 | 1.1849318 | 1.2007783 | 1.2167080 | 2.000000e+00 | 2.0000000 | 4.0000000 | -2.405483e-17 | -1.350771e-16 | 1.000000e+00 | -9.344377e-17 | 1.0000000 | 1.000000 | 1.00000000 | 1.000000 | 2.000000e+00 | 2 | 2.0 | 1 | 1 | 2 | 2 | 1.0 | 1.0 | 1.0 | 0 | 1 | 1.0 | EqualMeans_12_ASE |
| 701001902 | TAAKA VODKA 80 1L | 701001902 | 0.000000e+00 | 1.110223e-16 | not white noise | NA | 0.36038955 | 0.01000000 | 0.01000000 | not stationary | 1.2988034 | 1.3129060 | 1.3201709 | 1.4180342 | 1.4875214 | 1.5586325 | 1.7266422 | 1.8734829 | 1.9894017 | 2.0936752 | 2.1824864 | 2.2449573 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.8000000 | 1.3417939 | 1.3484977 | 1.3506908 | 1.3635321 | 1.4317118 | 1.5017399 | 1.6695923 | 1.8108711 | 1.9283069 | 2.0358965 | 2.1287877 | 2.1928990 | 3.7100420 | 2.9400814 | 2.4805010 | 2.2061830 | 2.0424458 | 1.9447130 | 1.8863775 | 1.8515577 | 1.8307742 | 1.8183687 | 1.8109641 | 1.8065443 | 1.367044e+00 | 1.4393103 | 1.4454570 | 1.2712999 | 1.3515299 | 1.4066517 | 1.4658585 | 1.5148079 | 1.6072195 | 1.7576524 | 1.8606205 | 1.9186453 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 3.9779756 | 2.1767938 | 1.9467462 | 1.9045347 | 1.7544638 | 1.7551391 | 1.7862844 | 1.8603817 | 1.9505741 | 1.9893415 | 2.0347064 | 2.0739335 | 2.1491457 | 2.624291e+00 | 3.4435520 | 3.0438653 | 2.816562e+00 | 1.619171e+00 | 2.475240e+00 | 2.363029e+00 | 3.2778318 | 1.212473 | 2.16253670 | 3.124322 | 5.095097e+00 | 2 | 2.0 | 2 | 4 | 2 | 3 | 5.0 | 3.0 | 3.0 | 1 | 2 | 2.0 | ARIMA_12_ASE |
| 700004770 | TAAKA VODKA 80 1L | 700004770 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.67246321 | 0.01000000 | 0.01000000 | not stationary | 2.9373276 | 2.9334814 | 2.4566438 | 2.3000840 | 2.2445583 | 2.2117293 | 2.0643972 | 1.9509494 | 1.8610028 | 1.8277122 | 1.8067681 | 1.7906182 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 3.3316667 | 2.7372199 | 2.7608743 | 2.6294740 | 2.5938914 | 2.5092408 | 2.5661585 | 2.6474384 | 2.7557645 | 2.9071031 | 3.0625002 | 3.0725270 | 3.1218363 | 2.9293446 | 2.9539608 | 2.9770709 | 2.9987670 | 3.0191356 | 3.0382579 | 3.0562102 | 3.0730642 | 3.0888869 | 3.1037414 | 3.1176871 | 3.1307795 | 3.295872e+00 | 2.7258590 | 2.6967588 | 2.7422302 | 2.7448767 | 2.7308850 | 2.8594171 | 3.0683988 | 3.2781511 | 3.5145773 | 3.5802386 | 3.7311803 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 2.9725420 | 15.3958816 | 15.8869049 | 15.9214910 | 15.3606947 | 15.1356711 | 14.9409582 | 14.6203682 | 14.6236395 | 14.4563891 | 14.2016280 | 13.3333187 | 12.5893127 | 1.306533e+00 | 4.7272362 | 2.0822285 | 1.381773e+00 | 2.634530e+00 | 4.847809e+00 | 3.027774e+00 | 2.1796301 | 2.307767 | 1.41588971 | 3.507124 | 1.584109e+00 | 4 | 4.0 | 3 | 1 | 2 | 2 | 4.0 | 2.0 | 3.0 | 1 | 2 | 5.0 | EqualMeans_12_ASE |
| 701000320 | TAAKA VODKA 80 1L | 701000320 | 7.397740e-02 | 1.020833e-01 | white noise | white noise | 0.02456406 | 0.01000000 | 0.10000000 | stationary | 0.3058120 | 0.2891453 | 0.2835897 | 0.2808120 | 0.2801709 | 0.2660684 | 0.2607570 | 0.2574145 | 0.2610826 | 0.2742735 | 0.2852991 | 0.2949145 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 0.4051081 | 0.3400124 | 0.3178584 | 0.3010784 | 0.3005917 | 0.2830615 | 0.2753256 | 0.2701542 | 0.2723935 | 0.2844376 | 0.2945231 | 0.3040786 | 1.1262931 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 1.1500000 | 3.367507e-01 | 0.3334983 | 0.3298248 | 0.3271361 | 0.3369339 | 0.3258995 | 0.3179715 | 0.3165767 | 0.3249886 | 0.3380303 | 0.3485719 | 0.3592423 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0000000 | 1.0951482 | 1.0391884 | 1.0373243 | 0.9956590 | 0.9750075 | 0.9688032 | 0.9617803 | 0.9495702 | 0.9384780 | 0.9410152 | 0.9327267 | 0.9238507 | -2.835440e-01 | 1.0000000 | 1.0000000 | 1.000000e+00 | 0.000000e+00 | 2.000000e+00 | 1.000000e+00 | 1.0000000 | 1.000000 | 1.00000000 | 1.000000 | 1.000000e+00 | 2 | 2.0 | 1 | 1 | 1 | 1 | 0.0 | 1.0 | 2.0 | 0 | 1 | 1.0 | EqualMeans_12_ASE |
| 700005926 | TAAKA VODKA 80 1L | 700005926 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.02043425 | 0.01000000 | 0.01000000 | inconclusive | 1.2773077 | 1.2785897 | 1.2738889 | 1.2734615 | 1.2670513 | 1.2888462 | 1.3058791 | 1.3186538 | 1.3055128 | 1.2732051 | 1.2467716 | 1.2067949 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.5333333 | 1.4330655 | 1.5153141 | 1.4548217 | 1.5009097 | 1.3966455 | 1.3343924 | 1.2841664 | 1.2087831 | 1.1483447 | 1.0884805 | 1.0262071 | 0.9793421 | 2.2002900 | 2.1617869 | 2.1255065 | 2.0913205 | 2.0591081 | 2.0287553 | 2.0001548 | 1.9732053 | 1.9478117 | 1.9238840 | 1.9013376 | 1.8800928 | 2.667315e+00 | 3.4118599 | 3.8792223 | 3.8945939 | 4.0508092 | 3.9659928 | 3.9156449 | 3.7875039 | 3.7042064 | 3.5755196 | 3.5150700 | 3.4031691 | 1.6954044 | 1.9238215 | 2.0300241 | 1.9299860 | 2.3085755 | 2.3687749 | 2.2688382 | 2.2545610 | 2.2051669 | 2.0706909 | 2.0700251 | 2.1066515 | 9.7833663 | 7.4145723 | 5.6429707 | 4.8216838 | 4.4154853 | 4.1634533 | 3.9056714 | 3.6334260 | 3.4048642 | 3.2365527 | 3.0866317 | 2.9483866 | 1.683491e+00 | 0.0158938 | 2.4608878 | 5.416634e-01 | 2.256431e+00 | 1.826491e+00 | 1.551416e+00 | 2.6000376 | 2.910352 | 2.25189453 | 3.394532 | 2.261570e+00 | 3 | 2.0 | 1 | 2 | 1 | 3 | 1.0 | 2.0 | 2.0 | 2 | 2 | 2.0 | ARMA_12_ASE |
| 701001800 | TAAKA VODKA 80 1L | 701001800 | 1.224362e-01 | 4.792812e-01 | white noise | white noise | 0.21045181 | 0.01000000 | 0.03920430 | not stationary | 0.3269444 | 0.3769444 | 0.3799359 | 0.4064316 | 0.4248932 | 0.4372009 | 0.4547833 | 0.4801496 | 0.4956054 | 0.5087393 | 0.5194852 | 0.5196795 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.3269444 | 0.3769444 | 0.3799359 | 0.4064316 | 0.4248932 | 0.4372009 | 0.4547833 | 0.4801496 | 0.4956054 | 0.5087393 | 0.5194852 | 0.5196795 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 0.8333333 | 3.715443e-01 | 0.4106859 | 0.4270984 | 0.4572844 | 0.4870052 | 0.5077215 | 0.5265536 | 0.5514860 | 0.5634607 | 0.5780082 | 0.5876334 | 0.5895793 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 0.8826079 | 1.7195772 | 1.7795639 | 1.6700771 | 1.6177478 | 1.5964515 | 1.5903798 | 1.5545462 | 1.5487558 | 1.5511204 | 1.5446621 | 1.5448047 | 1.5176862 | 8.789558e-01 | -0.2864555 | 1.7378374 | 3.338108e-01 | 1.039229e+00 | -1.243127e-01 | 1.210245e+00 | 0.2435835 | 1.099384 | 0.97692315 | 2.054678 | 1.121891e+00 | 1 | 2.0 | 1 | 2 | 0 | 1 | 2.0 | 2.0 | 1.0 | 1 | 1 | 1.0 | EqualMeans_12_ASE |
| 700003059 | TAAKA VODKA 80 1L | 700003059 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.01000000 | 0.01000000 | 0.01000000 | inconclusive | 1.3594872 | 1.3876923 | 1.3475214 | 1.3319231 | 1.3246154 | 1.2406838 | 1.1990476 | 1.1681410 | 1.1401140 | 1.1015385 | 1.0662471 | 1.0265812 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7333333 | 0.7822079 | 0.8905432 | 0.8879031 | 0.9104011 | 0.9222210 | 0.8704409 | 0.8534507 | 0.8295435 | 0.8112416 | 0.7765995 | 0.7437519 | 0.7113119 | 0.9216603 | 1.5009765 | 0.9665898 | 1.4078036 | 0.9958728 | 1.3314352 | 1.0134655 | 1.2682290 | 1.0223817 | 1.2153779 | 1.0249141 | 1.1707156 | 2.591532e+00 | 2.7108124 | 2.4617483 | 2.3576535 | 2.2807949 | 2.1356822 | 2.1222404 | 2.1004201 | 2.0960634 | 2.0576792 | 2.0084829 | 1.9710193 | 1.2748582 | 1.3430106 | 0.7381308 | 1.0936850 | 1.1334287 | 0.9515117 | 1.0499681 | 1.0673239 | 1.0129014 | 1.0399485 | 1.0466752 | 1.0304761 | 1.7414562 | 1.8158592 | 1.7079300 | 1.6763549 | 1.7339938 | 1.7245794 | 1.7257332 | 1.7230273 | 1.6985303 | 1.6307441 | 1.5755449 | 1.5202460 | -2.765066e-01 | 1.3644443 | 0.4884796 | 9.041992e-01 | 3.579109e+00 | 1.527870e+00 | 1.258682e+00 | 2.1668142 | 1.913767 | 1.70682274 | 1.791777 | -9.828707e-02 | 1 | 0.0 | 1 | 1 | 1 | 1 | 2.0 | 1.0 | 2.0 | 1 | 2 | 0.0 | ARMA_12_ASE |
| 701000360 | TAAKA VODKA 80 1L | 701000360 | 0.000000e+00 | 0.000000e+00 | not white noise | NA | 0.01782149 | 0.01000000 | 0.01000000 | inconclusive | 1.0547703 | 1.1156677 | 1.1445139 | 1.1615011 | 1.1998985 | 1.2030609 | 1.2641110 | 1.2986806 | 1.3393857 | 1.4147703 | 1.4755162 | 1.5616079 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7083333 | 0.7409955 | 0.6622150 | 0.7679869 | 0.7996367 | 0.8200111 | 0.8356037 | 0.8565329 | 0.9073472 | 0.9353860 | 1.0023231 | 1.0571398 | 1.1326307 | 1.2880147 | 1.9607699 | 1.5563160 | 1.5176694 | 1.4476984 | 1.3413498 | 1.2904318 | 1.2191043 | 1.1667074 | 1.1166898 | 1.0722279 | 1.0332015 | 6.671504e-01 | 0.6490383 | 0.7694516 | 0.8198088 | 0.8097014 | 0.8220716 | 0.8006063 | 0.8420725 | 0.8396961 | 0.8555306 | 0.8745281 | 0.9032365 | 1.5484043 | 2.2453039 | 2.0482803 | 2.0237832 | 2.1001411 | 2.0408910 | 2.0708135 | 2.0614928 | 2.0611865 | 2.0640606 | 2.0616581 | 2.0629336 | 0.8000180 | 0.7884722 | 0.8333405 | 0.8557746 | 0.8692351 | 0.8782087 | 0.8846184 | 0.8894258 | 0.8931648 | 0.8961560 | 0.8986033 | 0.9006428 | 1.280019e+00 | 1.6965226 | 1.0000000 | 0.000000e+00 | 2.000000e+00 | 0.000000e+00 | 2.000000e+00 | 1.0000000 | 1.000000 | 2.00000000 | 1.000000 | 3.000000e+00 | 1 | 2.0 | 1 | 1 | 2 | 1 | 3.0 | 0.0 | 2.0 | 3 | 2 | 3.0 | ARIMA_S12_12_ASE |
| 700004711 | TAAKA VODKA 80 1L | 700004711 | 1.225766e-01 | 5.601297e-01 | white noise | white noise | 0.34105678 | 0.01000000 | 0.01000000 | not stationary | 0.2550041 | 0.2575682 | 0.2569699 | 0.2547476 | 0.2537733 | 0.2535511 | 0.2547476 | 0.2746515 | 0.3067420 | 0.3466964 | 0.3926031 | 0.4436152 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.2550041 | 0.2575682 | 0.2569699 | 0.2547476 | 0.2537733 | 0.2535511 | 0.2547476 | 0.2746515 | 0.3067420 | 0.3466964 | 0.3926031 | 0.4436152 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 0.5166667 | 3.361097e-01 | 0.3155127 | 0.2919478 | 0.2764727 | 0.2586763 | 0.2496937 | 0.2544425 | 0.2763915 | 0.3005871 | 0.3288234 | 0.3599117 | 0.3946049 | 0.8174024 | 0.6424489 | 0.6798952 | 0.6718803 | 0.6735958 | 0.6732286 | 0.6733072 | 0.6732904 | 0.6732940 | 0.6732932 | 0.6732934 | 0.6732934 | 0.5959641 | 0.5948793 | 0.4870828 | 0.4477523 | 0.4126828 | 0.4140054 | 0.4148010 | 0.4167965 | 0.4173774 | 0.4165885 | 0.4219115 | 0.4476560 | 5.736152e-17 | 1.0000000 | 1.0000000 | 5.736152e-17 | 1.000000e+00 | 7.817820e-17 | 1.000000e+00 | 1.0000000 | 1.000000 | 1.00000000 | 1.000000 | 1.128727e-16 | 0 | 1.0 | 1 | 1 | 1 | 0 | 0.0 | 2.0 | 2.0 | 2 | 2 | 2.0 | ARIMA_12_ASE |
aggregated_forecast = results[c("Product_Type","Product","Customer","winning_12","ACTUAL_1","ACTUAL_2","ACTUAL_3","ACTUAL_4","ACTUAL_5","ACTUAL_6","ACTUAL_7","ACTUAL_8","ACTUAL_9","ACTUAL_10","ACTUAL_11","ACTUAL_12")]
for (i in 1:z){
if (results$winning_12[i] == "EqualMeans_12_ASE"){
aggregated_forecast$F1[i] <- results$EqualMeans_F1[i]
aggregated_forecast$F2[i] <- results$EqualMeans_F2[i]
aggregated_forecast$F3[i] <- results$EqualMeans_F3[i]
aggregated_forecast$F4[i] <- results$EqualMeans_F4[i]
aggregated_forecast$F5[i] <- results$EqualMeans_F5[i]
aggregated_forecast$F6[i] <- results$EqualMeans_F6[i]
aggregated_forecast$F7[i] <- results$EqualMeans_F7[i]
aggregated_forecast$F8[i] <- results$EqualMeans_F8[i]
aggregated_forecast$F9[i] <- results$EqualMeans_F9[i]
aggregated_forecast$F10[i] <- results$EqualMeans_F10[i]
aggregated_forecast$F11[i] <- results$EqualMeans_F11[i]
aggregated_forecast$F12[i] <- results$EqualMeans_F12[i]
} else if (results$winning_12[i] == "ARMA_12_ASE"){
aggregated_forecast$F1[i] <- results$ARMA_F1[i]
aggregated_forecast$F2[i] <- results$ARMA_F2[i]
aggregated_forecast$F3[i] <- results$ARMA_F3[i]
aggregated_forecast$F4[i] <- results$ARMA_F4[i]
aggregated_forecast$F5[i] <- results$ARMA_F5[i]
aggregated_forecast$F6[i] <- results$ARMA_F6[i]
aggregated_forecast$F7[i] <- results$ARMA_F7[i]
aggregated_forecast$F8[i] <- results$ARMA_F8[i]
aggregated_forecast$F9[i] <- results$ARMA_F9[i]
aggregated_forecast$F10[i] <- results$ARMA_F10[i]
aggregated_forecast$F11[i] <- results$ARMA_F11[i]
aggregated_forecast$F12[i] <- results$ARMA_F12[i]
} else if (results$winning_12[i] == "ARIMA_12_ASE"){
aggregated_forecast$F1[i] <- results$ARIMA_F1[i]
aggregated_forecast$F2[i] <- results$ARIMA_F2[i]
aggregated_forecast$F3[i] <- results$ARIMA_F3[i]
aggregated_forecast$F4[i] <- results$ARIMA_F4[i]
aggregated_forecast$F5[i] <- results$ARIMA_F5[i]
aggregated_forecast$F6[i] <- results$ARIMA_F6[i]
aggregated_forecast$F7[i] <- results$ARIMA_F7[i]
aggregated_forecast$F8[i] <- results$ARIMA_F8[i]
aggregated_forecast$F9[i] <- results$ARIMA_F9[i]
aggregated_forecast$F10[i] <- results$ARIMA_F10[i]
aggregated_forecast$F11[i] <- results$ARIMA_F11[i]
aggregated_forecast$F12[i] <- results$ARIMA_F12[i]
} else if (results$winning_12[i] == "ARIMA_S12_12_ASE"){
aggregated_forecast$F1[i] <- results$ARIMA_S12_F1[i]
aggregated_forecast$F2[i] <- results$ARIMA_S12_F2[i]
aggregated_forecast$F3[i] <- results$ARIMA_S12_F3[i]
aggregated_forecast$F4[i] <- results$ARIMA_S12_F4[i]
aggregated_forecast$F5[i] <- results$ARIMA_S12_F5[i]
aggregated_forecast$F6[i] <- results$ARIMA_S12_F6[i]
aggregated_forecast$F7[i] <- results$ARIMA_S12_F7[i]
aggregated_forecast$F8[i] <- results$ARIMA_S12_F8[i]
aggregated_forecast$F9[i] <- results$ARIMA_S12_F9[i]
aggregated_forecast$F10[i] <- results$ARIMA_S12_F10[i]
aggregated_forecast$F11[i] <- results$ARIMA_S12_F11[i]
aggregated_forecast$F12[i] <- results$ARIMA_S12_F12[i]
}
}
# other time series that did not have enough data points, will use mean for forecasts
zz = nrow(combinations_mean)
results_mean <- data.frame(Product_Type=integer(),
Product=character(),
Customer=integer(),
EqualMeans_F1=double(),
EqualMeans_F2=double(),
EqualMeans_F3=double(),
EqualMeans_F4=double(),
EqualMeans_F5=double(),
EqualMeans_F6=double(),
EqualMeans_F7=double(),
EqualMeans_F8=double(),
EqualMeans_F9=double(),
EqualMeans_F10=double(),
EqualMeans_F11=double(),
EqualMeans_F12=double(),
ACTUAL_1=double(),
ACTUAL_2=double(),
ACTUAL_3=double(),
ACTUAL_4=double(),
ACTUAL_5=double(),
ACTUAL_6=double(),
ACTUAL_7=double(),
ACTUAL_8=double(),
ACTUAL_9=double(),
ACTUAL_10=double(),
ACTUAL_11=double(),
ACTUAL_12=double(),
stringsAsFactors = FALSE)
# loop through sample combinations
for(i in 1:zz) {
sample_combinations1 = combinations_mean[i,]
temp1 = inner_join(temp_mean,sample_combinations1)
product = sample_combinations1$Product
customer = sample_combinations1$Customer_ID
product_type = sample_combinations1$Customer_ID
results_mean[i,"Product_Type"] = product_type
results_mean[i,"Product"] = as.character(sample_combinations1$Product)
results_mean[i,"Customer"] = customer
par(mfrow=c(1,1))
plot.ts(temp1$STD_Cases,
main=c(paste("Standard Case Sales of ", product),
paste("for Customer",customer)),
xlab="Months",
ylab="Standard Cases")
j=12
#Equal Means Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
sink()
assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
results_mean[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
results_mean[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
results_mean[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
results_mean[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
results_mean[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
results_mean[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
results_mean[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
results_mean[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
results_mean[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
results_mean[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
results_mean[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
results_mean[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
results_mean[i,paste0("EqualMeans_F1")] = model0_mean
results_mean[i,paste0("EqualMeans_F2")] = model0_mean
results_mean[i,paste0("EqualMeans_F3")] = model0_mean
results_mean[i,paste0("EqualMeans_F4")] = model0_mean
results_mean[i,paste0("EqualMeans_F5")] = model0_mean
results_mean[i,paste0("EqualMeans_F6")] = model0_mean
results_mean[i,paste0("EqualMeans_F7")] = model0_mean
results_mean[i,paste0("EqualMeans_F8")] = model0_mean
results_mean[i,paste0("EqualMeans_F9")] = model0_mean
results_mean[i,paste0("EqualMeans_F10")] = model0_mean
results_mean[i,paste0("EqualMeans_F11")] = model0_mean
results_mean[i,paste0("EqualMeans_F12")] = model0_mean
results_mean[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
results_mean[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
results_mean[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
results_mean[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
results_mean[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
results_mean[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
results_mean[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
results_mean[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
results_mean[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
results_mean[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
results_mean[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
results_mean[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]
}
results_mean$winning_12 = 'EqualMeans_12_ASE'
formattable(results_mean, align = c("l", rep("r", NCOL(table_a) - 1)))| Product_Type | Product | Customer | EqualMeans_F1 | EqualMeans_F2 | EqualMeans_F3 | EqualMeans_F4 | EqualMeans_F5 | EqualMeans_F6 | EqualMeans_F7 | EqualMeans_F8 | EqualMeans_F9 | EqualMeans_F10 | EqualMeans_F11 | EqualMeans_F12 | ACTUAL_1 | ACTUAL_2 | ACTUAL_3 | ACTUAL_4 | ACTUAL_5 | ACTUAL_6 | ACTUAL_7 | ACTUAL_8 | ACTUAL_9 | ACTUAL_10 | ACTUAL_11 | ACTUAL_12 | EqualMeans_1_ASE | EqualMeans_2_ASE | EqualMeans_3_ASE | EqualMeans_4_ASE | EqualMeans_5_ASE | EqualMeans_6_ASE | EqualMeans_7_ASE | EqualMeans_8_ASE | EqualMeans_9_ASE | EqualMeans_10_ASE | EqualMeans_11_ASE | EqualMeans_12_ASE | winning_12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 700005895 | TAAKA VODKA 80 1L | 700005895 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 0.4166667 | 1 | 2 | 0 | 2 | 2 | 0 | 2 | 2 | 2 | 2 | 2 | 2 | 0.4156197 | 0.4976709 | 0.5207479 | 0.5726709 | 0.6376709 | 0.6788675 | 0.7321032 | 0.7938248 | 0.8606339 | 0.9310043 | 1.0048970 | 1.0839957 | EqualMeans_12_ASE |
| 701000357 | TAAKA VODKA 80 1L | 701000357 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0.6166667 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.3264744 | 0.3328846 | 0.3350214 | 0.3367308 | 0.3403205 | 0.3444231 | 0.3473535 | 0.3495513 | 0.3512607 | 0.3526282 | 0.3537471 | 0.3546795 | EqualMeans_12_ASE |
| 700005867 | TAAKA VODKA 80 1L | 700005867 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 0.2250000 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0.2278045 | 0.2489583 | 0.2401976 | 0.2358173 | 0.2237019 | 0.2160524 | 0.2173649 | 0.2183494 | 0.2135595 | 0.2099840 | 0.2072917 | 0.2090011 | EqualMeans_12_ASE |
| 701001908 | TAAKA VODKA 80 1L | 701001908 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | 0.0000000 | EqualMeans_12_ASE |
aggregated_forecast_mean = results_mean[c("Product_Type","Product","Customer","winning_12","ACTUAL_1","ACTUAL_2","ACTUAL_3","ACTUAL_4","ACTUAL_5","ACTUAL_6","ACTUAL_7","ACTUAL_8","ACTUAL_9","ACTUAL_10","ACTUAL_11","ACTUAL_12")]
aggregated_forecast_mean$F1 <- results_mean$EqualMeans_F1
aggregated_forecast_mean$F2 <- results_mean$EqualMeans_F2
aggregated_forecast_mean$F3 <- results_mean$EqualMeans_F3
aggregated_forecast_mean$F4 <- results_mean$EqualMeans_F4
aggregated_forecast_mean$F5 <- results_mean$EqualMeans_F5
aggregated_forecast_mean$F6 <- results_mean$EqualMeans_F6
aggregated_forecast_mean$F7 <- results_mean$EqualMeans_F7
aggregated_forecast_mean$F8 <- results_mean$EqualMeans_F8
aggregated_forecast_mean$F9 <- results_mean$EqualMeans_F9
aggregated_forecast_mean$F10 <- results_mean$EqualMeans_F10
aggregated_forecast_mean$F11 <- results_mean$EqualMeans_F11
aggregated_forecast_mean$F12 <- results_mean$EqualMeans_F12
combined_aggregated_forecast <- rbind(aggregated_forecast, aggregated_forecast_mean)
combined_actuals_forecasts <- combined_aggregated_forecast %>% summarize_if(is.numeric,sum,na.rm=TRUE)
actuals <- combined_actuals_forecasts[c("ACTUAL_1","ACTUAL_2","ACTUAL_3","ACTUAL_4","ACTUAL_5","ACTUAL_6","ACTUAL_7","ACTUAL_8","ACTUAL_9","ACTUAL_10","ACTUAL_11","ACTUAL_12")]
actuals_trans <- transpose(actuals)
forecasts <- combined_actuals_forecasts[c("F1","F2","F3","F4","F5","F6","F7","F8","F9","F10","F11","F12")]
forecasts_trans <- transpose(forecasts)Forecast by Product (Aggregated)
# Filter dataset to only 1 product
df_taaka = df[df$Product == "TAAKA VODKA 80 1L",]
df_taaka_sum = aggregate(df_taaka$STD_Cases,by=list(Category=df_taaka$date),FUN=sum)
df_taaka_summarized <- df_taaka_sum %>% rename(date=Category,STD_Cases=x)resultsa <- data.frame(ljung_10=double(),
ljung_24=double(),
ljung_results=character(),
top_5_bic=character(),
ADF=double(),
PP=double(),
KPSS=double(),
stationarity_results=character(),
EqualMeans_1_ASE=double(),
EqualMeans_2_ASE=double(),
EqualMeans_3_ASE=double(),
EqualMeans_4_ASE=double(),
EqualMeans_5_ASE=double(),
EqualMeans_6_ASE=double(),
EqualMeans_7_ASE=double(),
EqualMeans_8_ASE=double(),
EqualMeans_9_ASE=double(),
EqualMeans_10_ASE=double(),
EqualMeans_11_ASE=double(),
EqualMeans_12_ASE=double(),
EqualMeans_F1=double(),
EqualMeans_F2=double(),
EqualMeans_F3=double(),
EqualMeans_F4=double(),
EqualMeans_F5=double(),
EqualMeans_F6=double(),
EqualMeans_F7=double(),
EqualMeans_F8=double(),
EqualMeans_F9=double(),
EqualMeans_F10=double(),
EqualMeans_F11=double(),
EqualMeans_F12=double(),
ARMA_1_ASE=double(),
ARMA_2_ASE=double(),
ARMA_3_ASE=double(),
ARMA_4_ASE=double(),
ARMA_5_ASE=double(),
ARMA_6_ASE=double(),
ARMA_7_ASE=double(),
ARMA_8_ASE=double(),
ARMA_9_ASE=double(),
ARMA_10_ASE=double(),
ARMA_11_ASE=double(),
ARMA_12_ASE=double(),
ARMA_F1=double(),
ARMA_F2=double(),
ARMA_F3=double(),
ARMA_F4=double(),
ARMA_F5=double(),
ARMA_F6=double(),
ARMA_F7=double(),
ARMA_F8=double(),
ARMA_F9=double(),
ARMA_F10=double(),
ARMA_F11=double(),
ARMA_F12=double(),
ARIMA_1_ASE=double(),
ARIMA_2_ASE=double(),
ARIMA_3_ASE=double(),
ARIMA_4_ASE=double(),
ARIMA_5_ASE=double(),
ARIMA_6_ASE=double(),
ARIMA_7_ASE=double(),
ARIMA_8_ASE=double(),
ARIMA_9_ASE=double(),
ARIMA_10_ASE=double(),
ARIMA_11_ASE=double(),
ARIMA_12_ASE=double(),
ARIMA_F1=double(),
ARIMA_F2=double(),
ARIMA_F3=double(),
ARIMA_F4=double(),
ARIMA_F5=double(),
ARIMA_F6=double(),
ARIMA_F7=double(),
ARIMA_F8=double(),
ARIMA_F9=double(),
ARIMA_F10=double(),
ARIMA_F11=double(),
ARIMA_F12=double(),
ARIMA_S12_1_ASE=double(),
ARIMA_S12_2_ASE=double(),
ARIMA_S12_3_ASE=double(),
ARIMA_S12_4_ASE=double(),
ARIMA_S12_5_ASE=double(),
ARIMA_S12_6_ASE=double(),
ARIMA_S12_7_ASE=double(),
ARIMA_S12_8_ASE=double(),
ARIMA_S12_9_ASE=double(),
ARIMA_S12_10_ASE=double(),
ARIMA_S12_11_ASE=double(),
ARIMA_S12_12_ASE=double(),
ARIMA_S12_F1=double(),
ARIMA_S12_F2=double(),
ARIMA_S12_F3=double(),
ARIMA_S12_F4=double(),
ARIMA_S12_F5=double(),
ARIMA_S12_F6=double(),
ARIMA_S12_F7=double(),
ARIMA_S12_F8=double(),
ARIMA_S12_F9=double(),
ARIMA_S12_F10=double(),
ARIMA_S12_F11=double(),
ARIMA_S12_F12=double(),
ACTUAL_1=double(),
ACTUAL_2=double(),
ACTUAL_3=double(),
ACTUAL_4=double(),
ACTUAL_5=double(),
ACTUAL_6=double(),
ACTUAL_7=double(),
ACTUAL_8=double(),
ACTUAL_9=double(),
ACTUAL_10=double(),
ACTUAL_11=double(),
ACTUAL_12=double(),
stringsAsFactors = FALSE)
# loop through sample combinations
i=1
temp1 = df_taaka_summarized
par(mfrow=c(1,1))
plot.ts(temp1$STD_Cases,
main="TAAKA VODKA 80 1L",
xlab="Months",
ylab="Standard Cases")
par(mfrow = c(2,2))
invisible(acf(temp1$STD_Cases, main="ACF"))
invisible(parzen.wge(temp1$STD_Cases))
invisible(acf(temp1$STD_Cases[0:length(temp1$date)/2], main="ACF for 1st Half of Series"))
invisible(acf(temp1$STD_Cases[(1+length(temp1$date)/2):length(temp1$date)], main="ACF for 2nd Half of Series"))
Obs 0.581064 0.2907099 0.09796717 -0.002900433 0.1054023 0.1422157 0.06115488 0.0360746 -0.1158591 -0.1599279 The Ljung-Box test with K=10 has a p-value of 2.322229e-06 .Obs 0.581064 0.2907099 0.09796717 -0.002900433 0.1054023 0.1422157 0.06115488 0.0360746 -0.1158591 -0.1599279 -0.1164521 -0.0414574 0.03658722 0.1325334 0.08610644 -0.1175143 -0.1852131 -0.1792189 -0.07936305 0.08417133 0.0944759 0.02650935 -0.07443002 -0.1870262 The Ljung-Box test with K=24 has a p-value of 1.124084e-05 . resultsa[i,"ljung_24"] = ljung_24$pval
if (ljung_10$pval < .05 & ljung_24$pval < .05){
print("Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise.")
resultsa[i,"ljung_results"] = "not white noise"
} else if (ljung_10$pval > .05 & ljung_24$pval < .05){
print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
resultsa[i,"ljung_results"] = "inconclusive"
} else if (ljung_10$pval < .05 & ljung_24$pval > .05){
print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
resultsa[i,"ljung_results"] = "inconclusive"
} else {
print("Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise.")
resultsa[i,"ljung_results"] = "white noise"
}[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."---------WORKING... PLEASE WAIT...
Five Smallest Values of bic sink()
for (row in 1:nrow(aic)) {
if(aic[row,1] == 0 & aic[row,2] == 0){
print("One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise.")
resultsa[i,"top_5_bic"] = "white noise"
}
}
# Tests for stationarity
# Augmented Dickey-Fuller
adf=tseries::adf.test(temp1$STD_Cases)
resultsa[i,"ADF"] = adf$p.value
# Phillips-Perron
pp=tseries::pp.test(temp1$STD_Cases)
resultsa[i,"PP"] = pp$p.value
# Kwiatkowski-Phillips-Schmidt-Shin
kpss=tseries::kpss.test(temp1$STD_Cases)
resultsa[i,"KPSS"] = kpss$p.value
if (adf$p.value < .05 & kpss$p.value > .05){
print("Both stationarity tests indicate this time series is stationary.")
resultsa[i,"stationarity_results"] = "stationary"
} else if (adf$p.value >= .05 & kpss$p.value <= .05){
print("Both stationarity tests indicate this time series is NOT stationary.")
resultsa[i,"stationarity_results"] = "not stationary"
} else {
print("Both tests for stationarity were inconclusive.")
resultsa[i,"stationarity_results"] = "inconclusive"
}[1] "Both tests for stationarity were inconclusive." j=12
#Equal Means Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
sink()
assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
resultsa[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
resultsa[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
resultsa[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
resultsa[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
resultsa[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
resultsa[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
resultsa[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
resultsa[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
resultsa[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
resultsa[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
resultsa[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
resultsa[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
resultsa[i,paste0("EqualMeans_F1")] = model0_mean
resultsa[i,paste0("EqualMeans_F2")] = model0_mean
resultsa[i,paste0("EqualMeans_F3")] = model0_mean
resultsa[i,paste0("EqualMeans_F4")] = model0_mean
resultsa[i,paste0("EqualMeans_F5")] = model0_mean
resultsa[i,paste0("EqualMeans_F6")] = model0_mean
resultsa[i,paste0("EqualMeans_F7")] = model0_mean
resultsa[i,paste0("EqualMeans_F8")] = model0_mean
resultsa[i,paste0("EqualMeans_F9")] = model0_mean
resultsa[i,paste0("EqualMeans_F10")] = model0_mean
resultsa[i,paste0("EqualMeans_F11")] = model0_mean
resultsa[i,paste0("EqualMeans_F12")] = model0_mean
#ARMA Model
trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],type="aic"))
model1_est = invisible(est.arma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 0,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
resultsa[i,paste0("ARMA_1_ASE")] = WindowedASE1
resultsa[i,paste0("ARMA_2_ASE")] = WindowedASE2
resultsa[i,paste0("ARMA_3_ASE")] = WindowedASE3
resultsa[i,paste0("ARMA_4_ASE")] = WindowedASE4
resultsa[i,paste0("ARMA_5_ASE")] = WindowedASE5
resultsa[i,paste0("ARMA_6_ASE")] = WindowedASE6
resultsa[i,paste0("ARMA_7_ASE")] = WindowedASE7
resultsa[i,paste0("ARMA_8_ASE")] = WindowedASE8
resultsa[i,paste0("ARMA_9_ASE")] = WindowedASE9
resultsa[i,paste0("ARMA_10_ASE")] = WindowedASE10
resultsa[i,paste0("ARMA_11_ASE")] = WindowedASE11
resultsa[i,paste0("ARMA_12_ASE")] = WindowedASE12
resultsa[i,paste0("ARMA_F1")] = forecasts$f[1]
resultsa[i,paste0("ARMA_F2")] = forecasts$f[2]
resultsa[i,paste0("ARMA_F3")] = forecasts$f[3]
resultsa[i,paste0("ARMA_F4")] = forecasts$f[4]
resultsa[i,paste0("ARMA_F5")] = forecasts$f[5]
resultsa[i,paste0("ARMA_F6")] = forecasts$f[6]
resultsa[i,paste0("ARMA_F7")] = forecasts$f[7]
resultsa[i,paste0("ARMA_F8")] = forecasts$f[8]
resultsa[i,paste0("ARMA_F9")] = forecasts$f[9]
resultsa[i,paste0("ARMA_F10")] = forecasts$f[10]
resultsa[i,paste0("ARMA_F11")] = forecasts$f[11]
resultsa[i,paste0("ARMA_F12")] = forecasts$f[12]
#ARIMA Model with d=1
nulldev()
temp2 = artrans.wge(temp1$STD_Cases,1)
dev.off()png
2 trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],type="aic"))
model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 1,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARIMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
resultsa[i,paste0("ARIMA_1_ASE")] = WindowedASE1
resultsa[i,paste0("ARIMA_2_ASE")] = WindowedASE2
resultsa[i,paste0("ARIMA_3_ASE")] = WindowedASE3
resultsa[i,paste0("ARIMA_4_ASE")] = WindowedASE4
resultsa[i,paste0("ARIMA_5_ASE")] = WindowedASE5
resultsa[i,paste0("ARIMA_6_ASE")] = WindowedASE6
resultsa[i,paste0("ARIMA_7_ASE")] = WindowedASE7
resultsa[i,paste0("ARIMA_8_ASE")] = WindowedASE8
resultsa[i,paste0("ARIMA_9_ASE")] = WindowedASE9
resultsa[i,paste0("ARIMA_10_ASE")] = WindowedASE10
resultsa[i,paste0("ARIMA_11_ASE")] = WindowedASE11
resultsa[i,paste0("ARIMA_12_ASE")] = WindowedASE12
resultsa[i,paste0("ARIMA_F1")] = forecasts$f[1]
resultsa[i,paste0("ARIMA_F2")] = forecasts$f[2]
resultsa[i,paste0("ARIMA_F3")] = forecasts$f[3]
resultsa[i,paste0("ARIMA_F4")] = forecasts$f[4]
resultsa[i,paste0("ARIMA_F5")] = forecasts$f[5]
resultsa[i,paste0("ARIMA_F6")] = forecasts$f[6]
resultsa[i,paste0("ARIMA_F7")] = forecasts$f[7]
resultsa[i,paste0("ARIMA_F8")] = forecasts$f[8]
resultsa[i,paste0("ARIMA_F9")] = forecasts$f[9]
resultsa[i,paste0("ARIMA_F10")] = forecasts$f[10]
resultsa[i,paste0("ARIMA_F11")] = forecasts$f[11]
resultsa[i,paste0("ARIMA_F12")] = forecasts$f[12]
#ARIMA Model with S=12
nulldev()
temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
dev.off()png
2 trainingSize = 60
ASEHolder1 = numeric()
ASEHolder2 = numeric()
ASEHolder3 = numeric()
ASEHolder4 = numeric()
ASEHolder5 = numeric()
ASEHolder6 = numeric()
ASEHolder7 = numeric()
ASEHolder8 = numeric()
ASEHolder9 = numeric()
ASEHolder10 = numeric()
ASEHolder11 = numeric()
ASEHolder12 = numeric()
for( k in 1:(84-(trainingSize + j) + 1))
{
sink("file")
model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],type="aic"))
model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-12))],p=model1$p,q=model1$q))
forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 12, d = 0,n.ahead = j,plot=FALSE)
ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
sink()
assign(paste("ARIMAS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
}
WindowedASE1 = mean(ASEHolder1)
WindowedASE2 = mean(ASEHolder2)
WindowedASE3 = mean(ASEHolder3)
WindowedASE4 = mean(ASEHolder4)
WindowedASE5 = mean(ASEHolder5)
WindowedASE6 = mean(ASEHolder6)
WindowedASE7 = mean(ASEHolder7)
WindowedASE8 = mean(ASEHolder8)
WindowedASE9 = mean(ASEHolder9)
WindowedASE10 = mean(ASEHolder10)
WindowedASE11 = mean(ASEHolder11)
WindowedASE12 = mean(ASEHolder12)
resultsa[i,paste0("ARIMA_S12_1_ASE")] = WindowedASE1
resultsa[i,paste0("ARIMA_S12_2_ASE")] = WindowedASE2
resultsa[i,paste0("ARIMA_S12_3_ASE")] = WindowedASE3
resultsa[i,paste0("ARIMA_S12_4_ASE")] = WindowedASE4
resultsa[i,paste0("ARIMA_S12_5_ASE")] = WindowedASE5
resultsa[i,paste0("ARIMA_S12_6_ASE")] = WindowedASE6
resultsa[i,paste0("ARIMA_S12_7_ASE")] = WindowedASE7
resultsa[i,paste0("ARIMA_S12_8_ASE")] = WindowedASE8
resultsa[i,paste0("ARIMA_S12_9_ASE")] = WindowedASE9
resultsa[i,paste0("ARIMA_S12_10_ASE")] = WindowedASE10
resultsa[i,paste0("ARIMA_S12_11_ASE")] = WindowedASE11
resultsa[i,paste0("ARIMA_S12_12_ASE")] = WindowedASE12
resultsa[i,paste0("ARIMA_S12_F1")] = forecasts$f[1]
resultsa[i,paste0("ARIMA_S12_F2")] = forecasts$f[2]
resultsa[i,paste0("ARIMA_S12_F3")] = forecasts$f[3]
resultsa[i,paste0("ARIMA_S12_F4")] = forecasts$f[4]
resultsa[i,paste0("ARIMA_S12_F5")] = forecasts$f[5]
resultsa[i,paste0("ARIMA_S12_F6")] = forecasts$f[6]
resultsa[i,paste0("ARIMA_S12_F7")] = forecasts$f[7]
resultsa[i,paste0("ARIMA_S12_F8")] = forecasts$f[8]
resultsa[i,paste0("ARIMA_S12_F9")] = forecasts$f[9]
resultsa[i,paste0("ARIMA_S12_F10")] = forecasts$f[10]
resultsa[i,paste0("ARIMA_S12_F11")] = forecasts$f[11]
resultsa[i,paste0("ARIMA_S12_F12")] = forecasts$f[12]
resultsa[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
resultsa[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
resultsa[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
resultsa[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
resultsa[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
resultsa[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
resultsa[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
resultsa[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
resultsa[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
resultsa[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
resultsa[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
resultsa[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]
#graph ASEs for each Model
EqualMeans_Results <- rbind(EqualMeans_Results_1,EqualMeans_Results_2,EqualMeans_Results_3,EqualMeans_Results_4,EqualMeans_Results_5,EqualMeans_Results_6,
EqualMeans_Results_7,EqualMeans_Results_8,EqualMeans_Results_9,EqualMeans_Results_10,EqualMeans_Results_11,EqualMeans_Results_12,
EqualMeans_Results_13)
ARMA_Results <- rbind(ARMA_Results_1,ARMA_Results_2,ARMA_Results_3,ARMA_Results_4,ARMA_Results_5,ARMA_Results_6,ARMA_Results_7,ARMA_Results_8,
ARMA_Results_9,ARMA_Results_10,ARMA_Results_11,ARMA_Results_12,ARMA_Results_13)
ARIMA_Results <- rbind(ARIMA_Results_1,ARIMA_Results_2,ARIMA_Results_3,ARIMA_Results_4,ARIMA_Results_5,ARIMA_Results_6,ARIMA_Results_7,ARIMA_Results_8,
ARIMA_Results_9,ARIMA_Results_10,ARIMA_Results_11,ARIMA_Results_12,ARIMA_Results_13)
ARIMAS_Results <- rbind(ARIMAS_Results_1,ARIMAS_Results_2,ARIMAS_Results_3,ARIMAS_Results_4,ARIMAS_Results_5,ARIMAS_Results_6,ARIMAS_Results_7,ARIMAS_Results_8,
ARIMAS_Results_9,ARIMAS_Results_10,ARIMAS_Results_11,ARIMAS_Results_12,ARIMAS_Results_13)
EqualMeans_Means <- colMeans(EqualMeans_Results)
ARMA_Means <- colMeans(ARMA_Results)
ARIMA_Means <- colMeans(ARIMA_Results)
ARIMAS_Means <- colMeans(ARIMAS_Results)
Combined_Means <- data.frame(EqualMeans_Means,ARMA_Means, ARIMA_Means, ARIMAS_Means)
Combined_Means$horizon <- as.numeric(row.names(Combined_Means))
g <- ggplot(data=Combined_Means, aes(horizon)) +
geom_line(aes(y=EqualMeans_Means, color="Equal Means"),size=1.5) +
geom_line(aes(y=ARMA_Means, color="ARMA"),size=1.5) +
geom_line(aes(y=ARIMA_Means, color="ARIMA"),size=1.5) +
geom_line(aes(y=ARIMAS_Means, color="ARIMAS"),size=1.5) +
scale_color_manual(values = c(
'Equal Means' = '#58508d',
'ARMA' = '#bc5090',
'ARIMA' = '#ff6361',
'ARIMAS' = '#ffa600'
)) +
labs(color='Models') +
scale_x_continuous(breaks=seq(0,13,1)) +
ggtitle(paste("Model ASEs for ", product,"and Customer",customer)) +
xlab("Month Ahead Forecast") +
ylab("ASE") +
theme(panel.background = element_blank(), axis.line = element_line(colour = "black"), legend.title = element_blank())
print(g)
resultsa$winning_12 <- colnames(resultsa[c("EqualMeans_12_ASE","ARMA_12_ASE","ARIMA_12_ASE","ARIMA_S12_12_ASE")])[apply(resultsa[c("EqualMeans_12_ASE","ARMA_12_ASE","ARIMA_12_ASE","ARIMA_S12_12_ASE")],1,which.min)]
formattable(resultsa, align = c("l", rep("r", NCOL(table_a) - 1)))| ljung_10 | ljung_24 | ljung_results | top_5_bic | ADF | PP | KPSS | stationarity_results | EqualMeans_1_ASE | EqualMeans_2_ASE | EqualMeans_3_ASE | EqualMeans_4_ASE | EqualMeans_5_ASE | EqualMeans_6_ASE | EqualMeans_7_ASE | EqualMeans_8_ASE | EqualMeans_9_ASE | EqualMeans_10_ASE | EqualMeans_11_ASE | EqualMeans_12_ASE | EqualMeans_F1 | EqualMeans_F2 | EqualMeans_F3 | EqualMeans_F4 | EqualMeans_F5 | EqualMeans_F6 | EqualMeans_F7 | EqualMeans_F8 | EqualMeans_F9 | EqualMeans_F10 | EqualMeans_F11 | EqualMeans_F12 | ARMA_1_ASE | ARMA_2_ASE | ARMA_3_ASE | ARMA_4_ASE | ARMA_5_ASE | ARMA_6_ASE | ARMA_7_ASE | ARMA_8_ASE | ARMA_9_ASE | ARMA_10_ASE | ARMA_11_ASE | ARMA_12_ASE | ARMA_F1 | ARMA_F2 | ARMA_F3 | ARMA_F4 | ARMA_F5 | ARMA_F6 | ARMA_F7 | ARMA_F8 | ARMA_F9 | ARMA_F10 | ARMA_F11 | ARMA_F12 | ARIMA_1_ASE | ARIMA_2_ASE | ARIMA_3_ASE | ARIMA_4_ASE | ARIMA_5_ASE | ARIMA_6_ASE | ARIMA_7_ASE | ARIMA_8_ASE | ARIMA_9_ASE | ARIMA_10_ASE | ARIMA_11_ASE | ARIMA_12_ASE | ARIMA_F1 | ARIMA_F2 | ARIMA_F3 | ARIMA_F4 | ARIMA_F5 | ARIMA_F6 | ARIMA_F7 | ARIMA_F8 | ARIMA_F9 | ARIMA_F10 | ARIMA_F11 | ARIMA_F12 | ARIMA_S12_1_ASE | ARIMA_S12_2_ASE | ARIMA_S12_3_ASE | ARIMA_S12_4_ASE | ARIMA_S12_5_ASE | ARIMA_S12_6_ASE | ARIMA_S12_7_ASE | ARIMA_S12_8_ASE | ARIMA_S12_9_ASE | ARIMA_S12_10_ASE | ARIMA_S12_11_ASE | ARIMA_S12_12_ASE | ARIMA_S12_F1 | ARIMA_S12_F2 | ARIMA_S12_F3 | ARIMA_S12_F4 | ARIMA_S12_F5 | ARIMA_S12_F6 | ARIMA_S12_F7 | ARIMA_S12_F8 | ARIMA_S12_F9 | ARIMA_S12_F10 | ARIMA_S12_F11 | ARIMA_S12_F12 | ACTUAL_1 | ACTUAL_2 | ACTUAL_3 | ACTUAL_4 | ACTUAL_5 | ACTUAL_6 | ACTUAL_7 | ACTUAL_8 | ACTUAL_9 | ACTUAL_10 | ACTUAL_11 | ACTUAL_12 | winning_12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2.322229e-06 | 1.124084e-05 | not white noise | NA | 0.3279525 | 0.01 | 0.1 | inconclusive | 4059.231 | 3679.643 | 3401.196 | 3372.65 | 3330.088 | 3663.9 | 4022.845 | 4369.204 | 4647.175 | 4822.214 | 4991.421 | 5189.347 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 387.7917 | 3173.814 | 3540.745 | 3475.842 | 3562.13 | 3495.253 | 3772.052 | 4094.861 | 4425.126 | 4696.629 | 4868.098 | 5034.353 | 5228.588 | 325.3383 | 350.9228 | 366.0264 | 374.9427 | 380.2064 | 383.3137 | 385.1482 | 386.2311 | 386.8704 | 387.2478 | 387.4706 | 387.6021 | 7105.365 | 12887.81 | 15588.65 | 18324.48 | 19097.58 | 18725.51 | 18836.91 | 20251.35 | 21113.27 | 21670.1 | 21527.4 | 20880.61 | 244.7304 | 221.902 | 207.9192 | 199.3544 | 194.1084 | 190.8951 | 188.9268 | 187.7213 | 186.9828 | 186.5305 | 186.2535 | 186.0838 | 7755.406 | 8228.346 | 9375.721 | 9464.392 | 9215.362 | 9205.438 | 9316.413 | 9585.313 | 9869.667 | 10090.96 | 10043.93 | 9989.717 | 416.2036 | 403.062 | 299.9213 | 407.1609 | 345.28 | 354.6572 | 399.4513 | 418.6447 | 443.691 | 404.1049 | 331.5171 | 281.7067 | 290.9 | 430 | 401 | 484 | 350.9 | 220 | 289.9 | 297.9 | 327.8 | 363.9 | 310 | 278.9 | EqualMeans_12_ASE |